Course and Exam Description Updated Fall 2017 AP® Physics 1: Algebra-Based Including: Course Framework and Sample Exam Questions

Updated Fall 2017 AP Physics 1: Algebra-Based Course and Exam Description Including: Course Framework and Sample Exam Questions

Effective Fall 2017 About the College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association is made up of over 6,000 of the world’s leading educational institutions and is dedicated to promoting excellence and equity in education. Each year, the College Board helps more than seven million students prepare for a successful transition to college through programs and services in college readiness and college success — including the SAT® and the Advanced Placement Program®. The organization also serves the education community through research and advocacy on behalf of students, educators, and schools. For further information, visit www.collegeboard.org.

AP® Equity and Access Policy The College Board strongly encourages educators to make equitable access a guiding principle for their AP programs by giving all willing and academically prepared students the opportunity to participate in AP. We encourage the elimination of barriers that restrict access to AP for students from ethnic, racial, and socioeconomic groups that have been traditionally underserved. Schools should make every effort to ensure their AP classes reflect the diversity of their student population. The College Board also believes that all students should have access to academically challenging course work before they enroll in AP classes, which can prepare them for AP success. It is only through a commitment to equitable preparation and access that true equity and excellence can be achieved.

AP Course and Exam Descriptions AP course and exam descriptions are updated regularly. Please visit AP Central® (apcentral.collegeboard.org) to determine whether a more recent course and exam description PDF is available.

© 2017 The College Board. College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. All other products and services may be trademarks of their respective owners. Visit the College Board on the Web: www.collegeboard.org.

ii Contents

1 About This Edition

2 Acknowledgments

3 About AP 3 Offering AP Courses and Enrolling Students 4 How AP Courses and Exams Are Developed 4 How AP Exams Are Scored 5 Using and Interpreting AP Scores 5 Additional Resources

6 About the AP Physics 1 Course 6 About This Course 6 College Course Equivalent 6 Prerequisites 6 The Laboratory Requirement

6 Participating in the AP Course Audit

9 The AP Physics 1: Algebra-Based Course Framework 9 Overview

11 Science Practices for AP Physics

16 Content Outline 16 Content Area 1: Kinematics 19 Content Area 2: Dynamics 25 Content Area 3: Circular Motion and Gravitation 32 Content Area 4: Energy 39 Content Area 5: Momentum 44 Content Area 6: Simple Harmonic Motion 47 Content Area 7: Torque and Rotational Motion 53 Content Area 8: Electric Charge and Electric Force 55 Content Area 9: DC Circuits 58 Content Area 10: Mechanical Waves and Sound

63 References

iii 64 The Laboratory Investigations 64 Inquiry Instruction in the AP Science Classroom

65 Expectations for Analysis of Uncertainty in Laboratory Investigations

65 Time and Resources

66 References

67 The AP Physics 1: Algebra-Based Exam 67 Exam Information 68 Student Work for Free-Response Sections 68 Terms Defined 69 The Paragraph-Length Response 70 Expectations for the Analysis of Uncertainty 70 Calculators and Equation Tables 71 Time Management

72 Sample Questions for the AP Physics 1 Exam 72 Multiple-Choice Questions 100 Answers to Multiple-Choice Questions 101 Free-Response Questions 106 Scoring Guidelines

Appendixes 112 Appendix A: The Big Ideas in AP Physics 1

119 Appendix B: Developing Big Ideas from Foundational Physics Principles

120 Appendix C: AP Physics 1 Equations and Constants

123 Contact Us

iv About This Edition This revised edition of the AP Physics 1: Algebra-Based Course and Exam Description provides a stand-alone course and exam description for the AP Physics 1 course. While the scope, sequence, and course content of AP Physics 1 has not changed, this revised edition provides a content outline of the course that is topically arranged. The content outline is also presented in a tabular format to more clearly show the relationships between enduring understandings, learning objectives, and essential knowledge statements. Additional conceptual information related to each enduring understanding and learning objective is included in the essential knowledge sections of the content outline. Relevant equations from the AP Physics 1 Equations and Constants tables have also been added to the essential knowledge sections so that teachers and students can see specific instances where they apply. The AP Physics 2 Course and Exam Description has also been revised in the same way.

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© 2017 The College Board Acknowledgments The College Board would like to acknowledge the following committee members, consultants, and reviewers for their assistance with and commitment to the development of this curriculum:

Members of the AP Physics 1 and 2 Curriculum Development and Assessment Committee Andrew Elby (co-chair), University of Maryland, College Park, MD Connie Wells (co-chair), Pembroke Hill School, Kansas City, MO Eugenia Etkina, Rutgers University, Newark, NJ Dolores Gende, Parish Episcopal School, Dallas, TX Nick Giordano, Auburn University, Auburn, AL Robert Morse, St. Albans School, Washington, DC Deborah Roudebush, Oakton High School, Vienna, VA Gay Stewart (co-chair), University of Arkansas, Fayetteville, AR

Consultants and Reviewers for the College Board Carlos Ayala, Sonoma State University, Rohnert Park, CA Richard Duschl, Pennsylvania State University State College, PA Bob Hilborn, University of Texas at Dallas, Dallas, TX Jose Mestre, University of Illinois at Urbana-Champaign, Urbana, IL Jim Pellegrino, University of Illinois, Chicago, IL Jeanne Pemberton, University of Arizona, Tucson, AZ Mark Reckase, Michigan State University, East Lansing, MI Nancy Songer, University of Michigan, Ann Arbor, MI Marianne Wiser, Clark University, Worcester, MA

Director, Curriculum and Content Development for AP Physics Trinna Johnson

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About AP The College Board’s Advanced Placement Program® (AP®) enables students to pursue college- level studies while still in high school. Through more than 30 courses, each culminating in a rigorous exam, AP provides willing and academically prepared students with the opportunity to earn college credit and/or advanced placement. Taking AP courses also demonstrates to college admission officers that students have sought out the most rigorous course work available to them. Each AP course is modeled upon a comparable college course, and college and university faculty play a vital role in ensuring that AP courses align with college-level standards. Talented and dedicated AP teachers help AP students in classrooms around the world develop and apply the content knowledge and skills they will need later in college. Each AP course concludes with a college-level assessment developed and scored by college and university faculty as well as experienced AP teachers. AP Exams are an essential part of the AP experience, enabling students to demonstrate their mastery of college-level course work. Most four-year colleges and universities in the United States and universities in more than 60 countries recognize AP in the admission process and grant students credit, placement, or both on the basis of successful AP Exam scores. Visit www.collegeboard.org/apcreditpolicy to view AP credit and placement policies at more than 1,000 colleges and universities. Performing well on an AP Exam means more than just the successful completion of a course; it is a gateway to success in college. Research consistently shows that students who receive a score of 3 or higher on AP Exams typically experience greater academic success in college and have higher graduation rates than their non-AP peers.1 Additional AP studies are available at www.collegeboard.org/research.

Offering AP Courses and Enrolling Students This AP Course and Exam Description details the essential information required to understand the objectives and expectations of an AP course. The AP Program unequivocally supports the principle that each school implements its own curriculum that will enable students to develop the content knowledge and skills described here. Schools wishing to offer AP courses must participate in the AP Course Audit, a process through with AP teachers’ syllabi are reviewed by college faculty. The AP Course Audit was created to provide teachers and administrators with clear guidelines on curricular and resource requirements for AP courses and to help colleges and universities validate courses marked “AP” on students’ transcripts. This process ensures that AP teachers’ syllabi meet or exceed the curricular and resource expectations that college and secondary school faculty have established for college-level courses. For more information on the AP Course Audit, visit www.collegeboard.org/apcourseaudit. The College Board strongly encourages educators to make equitable access a guiding principle for their AP programs by giving all willing and academically prepared students the opportunity to participate in AP. We encourage the elimination of barriers that restrict access to AP for students from ethnic, racial, and socioeconomic groups that have been traditionally

1 See the following research studies for more details: Linda Hargrove, Donn Godin, and Barbara Dodd, College Outcomes Comparisons by AP and Non-AP High School Experiences (New York: The College Board, 2008). Chrys Dougherty, Lynn Mellor, and Shuling Jian, The Relationship Between Advanced Placement and College Graduation (Austin, Texas: National Center for Educational Accountability, 2006).

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underserved. The College Board also believes that all students should have access to academically challenging course work before they enroll in AP classes, which can prepare them for AP success. It is only through a commitment to equitable preparation and access that true equity and excellence can be achieved.

How AP Courses and Exams Are Developed AP courses and exams are designed by committees of college faculty and expert AP teachers who ensure that each AP subject reflects and assesses college-level expectations. A list of each subject’s current AP Development Committee members is available on apcentral.collegeboard.org. AP Development Committees define the scope and expectations of the course, articulating through a course framework what students should know and be able to do upon completion of the AP course. Their work is informed by data collected from a range of colleges and universities to ensure that AP coursework reflects current scholarship and advances in the discipline. The AP Development Committees are also responsible for drawing clear and well-articulated connections between the AP course and AP Exam — work that includes designing and approving exam specifications and exam questions. The AP Exam development process is a multi-year endeavor; all AP Exams undergo extensive review, revision, piloting, and analysis to ensure that questions are high quality and fair and that there is an appropriate spread of difficulty across the questions. Throughout AP course and exam development, the College Board gathers feedback from various stakeholders in both secondary schools and higher education institutions. This feedback is carefully considered to ensure that AP courses and exams are able to provide students with a college-level learning experience and the opportunity to demonstrate their qualifications for advanced placement.

How AP Exams Are Scored The exam scoring process, like the course and exam development process, relies on the expertise of both AP teachers and college faculty. While multiple-choice questions are scored by machine, the free-response questions are scored by thousands of college faculty and expert AP teachers at the annual AP Reading. AP Exam Readers are thoroughly trained, and their work is monitored throughout the Reading for fairness and consistency. In each subject, a highly respected college faculty member fills the role of Chief Reader, who, with the help of AP readers in leadership positions, maintains the accuracy of the scoring standards. Scores on the free-response questions are weighted and combined with the results of the computer- scored multiple-choice questions, and this raw score is converted into a composite AP score of 5, 4, 3, 2, or 1. The score-setting process is both precise and labor intensive, involving numerous psychometric analyses of the results of a specific AP Exam in a specific year and of the particular group of students who took that exam. Additionally, to ensure alignment with college-level standards, part of the score-setting process involves comparing the performance of AP students with the performance of students enrolled in comparable courses in colleges throughout the United States. In general, the AP composite score points are set so that the lowest raw score need to earn an AP score of 5 is equivalent to the average score among college students earning grades of A in the college course. Similarly, AP Exam scores of 4 are equivalent to college grades of A−, B+, and B. AP Exam scores of 3 are equivalent to college grades of B−, C+, and C.

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Using and Interpreting AP Scores The extensive work done by college faculty and AP teachers in the development of the course and the exam and throughout the scoring process ensures that AP Exam scores accurately represent students’ achievement in the equivalent college course. While colleges and universities are responsible for setting their own credit and placement policies, AP scores signify how qualified students are to receive college credit or placement:

AP Score Qualification

5 Extremely well qualified

4 Well qualified

3 Qualified

2 Possibly qualified

1 No recommendation

Additional Resources Visit apcentral.collegeboard.org for more information about the AP Program.

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About the AP Physics 1 Course

About This Course AP Physics 1 is an algebra-based, introductory college-level physics course. Students cultivate their understanding of Physics through inquiry-based investigations as they explore these topics: kinematics; dynamics; circular motion and gravitation; energy; momentum; simple harmonic motion; torque and rotational motion; electric charge and electric force; DC circuits; and mechanical waves and sound.

College Course Equivalent AP Physics 1 is a full-year course that is the equivalent of a first-semester introductory college course in algebra-based physics.

Prerequisites There are no prerequisite courses. Students should have completed geometry and be concurrently taking Algebra II or an equivalent course. Although the Physics 1 course includes basic use of trigonometric functions, this understanding can be gained either in the concurrent math course or in the AP Physics 1 course itself.

The Laboratory Requirement This course requires that 25 percent of the instructional time be spent in hands-on laboratory work, with an emphasis on inquiry-based investigations that provide students with opportunities to demonstrate the foundational physics principles and apply all seven science practices defined in the course framework. Colleges may require students to present their laboratory materials from AP science courses before granting college credit for laboratory work, so students should be encouraged to retain their laboratory notebooks, reports, and other materials.

Participating in the AP Course Audit Schools wishing to offer AP courses must participate in the AP Course Audit. Participation in the AP Course Audit requires the online submission of two documents: the AP Course Audit form and the teacher’s syllabus. The AP Course Audit form is submitted by the AP teacher and the school principal (or designated administrator) to confirm awareness and understanding of the curricular and resource requirements. The syllabus, detailing how course requirements are met, is submitted by the AP teacher for review by college faculty.

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Please visit http://www.collegeboard.com/html/apcourseaudit/courses/physics_1.html for more information to support syllabus development including:

nn Annotated Sample Syllabi — Provide examples of how the curricular requirements can be demonstrated within the context of actual syllabi. nn Curricular and Resource Requirements — Identifies the set of curricular and resource expectations that college faculty nationwide have established for a college-level course. nn Example Textbook List — Includes a sample of AP college-level textbooks that meet the content requirements of the AP course. nn Syllabus Development Guide — Includes the guidelines reviewers use to evaluate syllabi along with three samples of evidence for each requirement. This guide also specifies the level of detail required in the syllabus to receive course authorization. nn Syllabus Development Tutorial — Describes the resources available to support syllabus development and walks through the syllabus development guide requirement by requirement.

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explicitly articulate the behaviors in which students need to in which students need to the behaviors articulate explicitly Interactions between systems can result in changes in between changes in systems result can Interactions systems.those are interactions of occur as a result that Changes constrained by conservation laws. from one momentum energy and transfer can Waves location to another without the permanent transfer of mass description of the for model serve and asmathematical a other phenomena. Objects and systems have properties systems have Objects as mass and and such structure. Systems internal may have charge. space explain be can used existing in Fields to interactions. be objects can other with object an of The interactions described by forces.

AP Science Practices engage in order to achieve conceptual understanding in the course. The science practices The science practices in the course. conceptual understanding to achieve in order engage testable and refine and use them lines of evidence students to establish to develop enable and reasoning inquiry, phenomena. Because content, of natural and predictions explanations outline described in the content objective each learning important in AP Physics, equally are skills described in the science practices. with inquiry and reasoning combines content Course and Exam Description and Exam Course Overview The A table that illustrates how the foundational physics principles support the development of of support the principles development physics the how foundational that illustrates A table B. these big ideas is in Appendix Big Idea 5: Big Idea 6:Big Big Idea 3: Big Idea 4: Big Big Idea 1: Big Idea 2:Big Based on the Understanding by Design (Wiggins and McTighe) model, the AP Physics 1 the model, Physics 1 AP and McTighe) Design (Wiggins by Based on the Understanding description of the and detailed course a clear to provide is intended framework course students must what specifies The framework student success. necessary for requirements students to make instruction that allows and encourages and understand, to do, be able know, world. of thinking about the physical way a broader domains through connections across encompass core which of physics, “big ideas” six around is structured framework This course for a complete Appendix A of the discipline. See and processes theories, scientific principles, big ideas: of the following presentation The AP Physics 1: Algebra-Based 1: The AP Physics Course Framework 9 10 Course Framework are asfollows: These content areas are presented inatabularformat. content Thecomponentsofthe outline Motion; Electric Charge andElectric Force; DCCircuits; andMechanicalWaves andSound. Motion andGravitation; Energy; Momentum;Simple HarmonicMotion;Torque andRotational the course,define topically arranged into10content areas: Kinematics; Dynamics;Circular The AP Physics 1:Algebra-Based Overview n n n n n n n n n n Enduring understandings are numbered tocorrespond appropriate the with bigidea. specifywhatthat astudentwillcometounderstand key aboutthe conceptsineachcourse. contentexploring the andskills. Theseunderstandings are expressed asgeneralizations These are long-term the takeaways related astudentshould bigideasthat retain tothe after Enduring understandings: focus pointsfor topiccovered. the Big ideas statements where appropriate. applied ineachcourse. Boundary statements endofessentialknowledge appear at the contextualthe differencesthe samebigideasandenduringunderstandings ofhow are content boundariesfor APPhysics the 1and2courses. Thesestatements helparticulate Boundary statements: understanding, andlearning objective. knowledge statements are numbered tocorrespond appropriate the with bigidea,enduring correct doneedtoknow inthe but they whenandhow tousethem context. Essential equations are provided exam, tostudentsat studentsdonotneedtomemorizethem, the tables (Appendix C)are provided toshow where are they applicable. Sincethese learning objective. Relevant equations from APPhysics the 1Equations andConstants astudentshouldthat know andbeable torecall inorder todemonstrate mastery ofeach essential knowledge statements. Thesestatements facts andbasicconcepts describethe Essential knowledge: correspond appropriate the with bigideaandenduringunderstanding (e.g., LO serve astargets ofassessmentfor eachcourse. Learningobjectives are numbered to to beable todoinorder todevelop enduringunderstandings. the Thelearning objectives corresponding learning objectives. Thelearning objectives convey what astudentneeds Learning objectives: within bracketswithin (e.g., EU).Thesciencepracticesto that learning objective aligntothe that are alsodesignated from BigIdea5,EnduringUnderstanding 5.F, first andisthe learning objective aligned content outline : Eachcontent are bigideasthat area particular main alistofthe the beginswith in this framework inthis key containsthe conceptsandrelated content that [SP 2.1,2.2,7.2] Aligned to the rightofeachlearning objective Alignedtothe are corresponding the Aligned to the rightofeachenduringunderstandingAligned tothe are the Thesestatements provide guidancetoteachers regarding the

Course andExam Description The firstthe the table lists columnof ). Return to Table ofContents

Course Framework 11

Return to Table of Contents Table © 2017 The College Board Return to Table of Contents Table to Return Science Practices for AP Physics AP Physics for Practices Science AP Physics 1: Algebra-Based AP Physics

The student can use mathematics appropriately. mathematics use can The student in the domain. The student can use representations and models to analyze situations or solve problems qualitatively and quantitatively. The student can reexpress key elements of natural phenomena across multiple representations The student can describe representations and models natural of or man-made phenomena and systems in the domain. The student can refine representationsand models natural of or man-made phenomena and systems in the domain. The student can create representations and models natural of or man-made phenomena and systems in the domain.

Course and Exam Description and Exam Course Physicists commonly use mathematical representations to describe and explain phenomena to describe and explain phenomena representations use mathematical commonly Physicists want we with When students work these representations, problems. as to solve as well the thethem description, the mathematical connections between to understand physical When using in the descriptions. mathematical phenomena, and the concepts represented using a why to justify students need to be able representations, or mathematical equations of the as to be aware is useful as well a particular situation to analyze particular equation can be used. Students conditions under which the equations/mathematical representations they need to a problem, When solving representations. too much on mathematical to rely tend representations, including picture ways, in multiple situation to describe thebe able problem 1.4 1.5 Practice 2: Science 1.2 1.3 1.1 The real world is extremely complex. When physicists describe and explain phenomena, they and explain phenomena, they describe When physicists complex. is extremely world The real These manageable. the analysis to make and processes systems, objects, try to simplify real model A simple will occur. phenomena new how used to predict are or models simplifications and behavior. structure internal the as an object, neglecting system’s a system treat may can A process such as an ideal gas. of objects, models of a system models are complex More the we consider only process when of a simplified fall is an example be simplified, too; free of the object with the Earth.interaction both Models can be and mathematical. conceptual as a steady the model, while of a mathematical model of a current is an example law Ohm’s with randomly move particles is a conceptual model (the particles charged of charged flow model, a good to make Basically, a particular in direction). some net motion [drift] of particles of a phenomenon or system one needs to identify a set of the most important characteristics is invent in the construction of models that physicists Inherent simplify analysis. that may physics introductory used to model of representations Examples the use of representations. diagrams. and ray bar charts, energy graphs, diagrams, force motion diagrams, pictures, are help Representations another example. are as equations such representations Mathematical here An example ideas. and communicating phenomena, making predictions, in analyzing of the expression mathematical to develop diagram force and a is using a motion diagram problem. a dynamics to solve in component form second law Newton’s The student can use representations and models to to Science models and Practice representations use can The student 1: problems. scientific solve and phenomena scientific communicate Science Practices AP for Physics important of the aspects that engage scientists work capture that follow practices The science will see teachers AP Physics students. of AP Physics expected of competence thein, at level and with content, the course integrated are these how practices within the objectives learning mind. in to design instruction withthey will be able these practices 11 12 Course Framework focus ofalearning objective. simple mathematical routines may beneededtoarrive at aresult even are they though notthe of afreely falling object—should raise flagsinstudents’ minds. Inmany physics situations, Science Practices for APPhysics example, obtaining35m/s should alsobeable toevaluate numerical result the interms itmakes ofwhether sense.For inverse proportionalities, etc.)andcause-and-effect the physicalrelations in world. They should beable totranslate between functionalrelations inequations (proportionalities, can bepredicted qualitatively problem quantitiesinthe ifoneofthe iszero orinfinity? They obtained interms ofunitsandlimitingcaseanalysis: equation lead Doesthe toresults that substitutethey values. They alsoshould beable toevaluate answer equation(s) andthe the addition, studentsshould algebraic beable the towork with form equation before ofthe instead offirst choosinga formula whose variablesthe givens match the problem. in In force diagrams, chooseanappropriate andsoon,then mathematical representation, AP Physics 1:Algebra-Based 3.3 3.2 3.1 data andfindings. a simple pendulumdepend?”by evaluating designingandcarryingoutexperimentsthen can lead to how one goes aboutevaluating questionssuchas, periodof “Uponwhat doesthe motion, leading toadiscussionoftime,angle (amplitude),andmass. Follow-up discussions first considerinwhat ways onecanmeasure physical quantities relevantthe pendulum’s to to relevant Asafirst modelsandtheories. step to thisquestion,studentsmightrefining build, studentsneedtobeguidedtoward refining “fuzzy”questionsand relating questions pointfrom isastarting this ask, “How whichateacher highdoesitswing?”Although may When asked what mightwant they tofindoutaboutasimple pendulum,somestudentsmay to learn. Even asimple physics within topic,posingascientificquestioncanbedifficult. instructional andcognitivescientific questionsisanimportant goal, albeitadifficultskill societalproblem.important Thus, helpingstudentslearn how topose,refine, and evaluate At opposite spectrum,somestudentsmay the endofthe believe science cansolve that every objects is9.8m/s compiling andpassingdown alarge body ofknown facts (e.g., acceleration the offree-falling point since,dependingonhow ascienceclassistaught,itmay scienceisabout seemthat Research scientistsposeandanswer meaningfulquestions. Studentsmay easily missthis thinking or to guide investigations within the context of course. the AP student The can 3: engage in scientific questioning Practice extend to Science 2.3 2.2 2.1

The student can evaluate scientific questions. scientific evaluate can student The questions. scientific refine can student The questions. scientific pose can student The phenomena. quantities numerically estimate can student The phenomena. natural describe that quantities to routines mathematical apply can student The problems. solve to routine ofamathematical the selection justify can student The 2 ; 2 for acceleration the ofabus—aboutfour acceleration timesthe ).

Course andExam Description

Course Framework 13

The student can collect data to answer a particular scientific question. The student can evaluate sources data of to answer a particular scientific question. The student can justify the selection the of kind data of needed to answer a particular scientific question. The student can design a plan for collecting data to answer a particular scientific question.

Course and Exam Description and Exam Course Students often think that to make a graph theythe need to connect or that points the data a graph think that to make Students often curve it is important can construct a best-fit that they Thus, linear. function is always best-fit or exponential functions). (such as quadratic relationship that do not fit a linear data for even whose size depends on the points as intervals data to represent be able Students should in this need to ask why the data, they students find a pattern After experimental uncertainty. When dealing that they have. and try to explain it using the knowledge is present pattern of the explanation pattern a testable to devise with be able phenomenon, they a new should 4.3 4.4 of Science Practice evaluation and perform can The 5: analysis student data evidence. 4.1 4.2 The student can plan and implement data collection collection data Science Practice implement and plan can 4: The student question. scientific a particular to relation in strategies scientific e.g., investigations, sources, different many from be collected can Data [Note: data.] archived and/or reconstruction, historic of others, observations, the findings from specificity, well as in as to narrow, broad scope from in range can Scientific questions posed question The mechanism. determining to and/orcauses factors influencing determining data. for collecting and will influence the plan the to be collected type of data will determine caused the whereas question is “What extinction of the dinosaurs?” of a broad An example does the pendulum depend?” Both is “Upon what one period of a simple questions a narrow “An asteroid be former might to and/orthe causes; an answer factors influencing ask for to the latter an answer collision with Earth whereas caused the extinction of the dinosaurs,” the cause test depends on themight be “The period mass and length of the To pendulum.” mass and length ascertain to if vary period, an experimental plan might of the pendulum’s so as variables to control indeed influence the period of a pendulum, taking care these factors or both influence be thethe period. A question could other, whether one factor, to determine does become extinct?” or “How the did “How dinosaurs posed to ask about mechanism, e.g., the pendulum depend on the period of a simple mass and length?” In the second question, and length of a mass, period, between relationship a mathematical the object is to determine is strategies collection experimental designs and/or data pendulum. Designing and improving some find might experiment pendulum a in students among discussion class A skill. learned a and divided timed 10 round-trips others while round-trip, a single the time for who measured uncertainty and assumptions of measurement issues 10. Such discussions can reveal by and using data of collecting that theabout the result motion. Students need to understand not a single a question is best thought to of as an interval, answer a numerical to determine of uncertainty is due to a combination the experimental uncertainty, This interval, number. Although error detailed the of taking in the measurement. instruments used and the process some idea, it is important that make students this pivotal is not necessary to convey analysis point data of a measured within the which they know value of the interval estimate reasoned this clear. that makes in a way their results and express 13 14 Course Framework for canreject experimentsthat ofscience. explanations heart andclaimsisat the explanation; alternate given explanations ofthe outcome canalways beformulated. Looking the prediction, outcomeconfirms this experimentdoesnotdisprovethe itonlythat means the prediction, outcomedoesnotmatch the explanationthe islikely the tobefalse. By contrast, if in openairandavacuum jar. claimiscorrect, Ifthe liquidshould dryfaster the inair. If same liquiddriesintwo conditions:test candesignan experimentinwhichthe claimthey the outcomes. For example, studentsmay liquidsdrybecauseairabsorbsmoisture. that think To to designexperimentstest alternative explanations ofphenomenaby comparingpredicted predictedthe andmeasured current. This procedure tests claim.Studentsshould beable the voltage,measuring the linearrelationship usingthe topredict current, the andcomparing through it.Theclaimcanbetested by resistors connectingother circuit, orlightbulbsinthe based ondata from anexperimentvarying voltage across aresistor andmeasuringcurrent current claimthat the isdirectly proportional topotential difference across conductors experimentaldesignbasedonan explanationparticular oraclaimunderscrutiny. Consider claimorexplanation tomakethe predictions. Aprediction states expected the outcomeofa offer evidence, toconstruct reasoned arguments their claimfromfor the evidence, andtouse evidence andachainofreasoning.need tobackitupwith Studentsshould beprepared to not aclaim,buttosay sameacceleration the allobjectsfall that with isaclaim,asonewould constitutethat direct andsimple observational evidence. To say all objects fall that down is frameworkIn this word the “claim” meansany answer astudent provides that except those difference betweentheories. explanations and molecular theory, quantumtheory, andatomic theory. Studentsshould understand the range the within theory. ofapplicabilitythe Examples inphysics oftheories includekinetic set ofphenomenaandgives are accounts that consistent multiple experimentaloutcomes with predictions usesaunifiedapproach aboutanew phenomenon.Atheory toaccount for alarge phenomenon, needstobeexperimentally testable. Oneshould beable touseitmake interaction liquid.Ascientificexplanation, accounting between andthe them for anobserved can leave negative kineticenergy the liquidsiftheir ishigherthan potential energy of exerted mass. acertain Liquidsdryupbecauserandomly onanobjectwith moving molecules Science Practices for APPhysics 5.2 5.1 anomalous. should beable torevise reasoning their new data, data for basedonthe that somemay appear asintervalsby both writingthem andnotassingle, absolute numbers. Finally, students checkforquantity andthen consistency across two measurements, the comparingtwo results uncertainty. Studentsshould beable todesignasecondexperimentdetermine same the do notproduce exact measurements andlearn what steps cantake they todecrease the if possible (see AP Physics 1:Algebra-Based expressed as describe amechanismthrough phenomenonoccurs. whichaparticular Newton’s secondlaw, Scientific explanations may specifyacause-and-effect relationship between variables or and theories. student The 6: can work with scientificexplanations Practice Science 5.3

analysis. data on based measurements and observations refine can student The relationships. or patterns identify to data analyze can student The particular scientific question. scientific particular a to relation in sets data by provided evidence the evaluate can student The ). It is important that studentsunderstand that 6.4).Itisimportant Practice instruments that Science , gives acceleration the observed whenagiven combination offorces is

Course andExam Description

Course Framework 15

The student can connect phenomena and models across spatial and temporal scales. The student can connect concepts in and across domain(s) to generalize or extrapolate in and/or across enduring understandings and/or big ideas. The student can evaluate alternative scientific explanations. The student can articulatethe reasons that scientific explanations and theories are refined or replaced. The student can make claims and predictions about natural phenomena based on scientific theories and models. The student can justify claims with evidence. The student can construct explanations phenomena of based on evidence produced through scientific practices.

Course and Exam Description and Exam Course 7.1 7.2 6.5 across knowledge relate Science and connect Practice to able is The student 7: across domains. and in representations various scales, concepts, and disciplinary boundaries their across learning the opportunity to transfer have Students should the sciences the to link, synthesize, across able they ideas apply and learn so that they are contexts multiple that providing indicates learn people on how Research and mathematics. knowledge students to bundle this allows transfer; facilitates to which major ideas apply also be should Students to which it applies. in memory together with the contexts multiple and ideas do not to which major concepts contexts appropriate seemingly to recognize able students should of mechanics, in the context laws conservation various learning After apply. the idea and extend physics means in the to describe what concept of conservation be able high-energy mean at of energy might conservation what example, For to other contexts. major role? a plays equivalence mass–energy Einstein’s where with collisions, scales particle about arguments mean when constructing or evaluating of energy does conservation What across physics from ideas apply in which students may Another context warming? global on Earth with coupled the is the life notion of and time scales origin of human spatial vast of time the of the If one views age Earth to a year life. in analogy intelligent extraterrestrial on Earth began 1, then 1991) with life & Cummins, the on January (see Ritger Earth formed on 6; mammals appeared on November appeared 5; multicellular organisms April around 28 minutes on December 31 just appeared humans most amazingly, December 23. Perhaps outside our life intelligent seeking the of this implications for are midnight. What before on an life of finding intelligent of the probability estimate is a reasonable What solar system? and how observations, astronomical through planet that might discover scientists earthlike to answer not expected Although students are those about making does one go estimates? to talk be able they should AP science course, a single questions after complex these very about them using the concepts they learned. intelligently 6.3 6.4 6.1 6.2 15 Content Outline Content Area 1: Kinematics

Content Outline Content Area 1: Kinematics ramework F Big Idea 3: The interactions of an object with other objects can be described by forces.

Course Course Big Idea 4: Interactions between systems can result in changes in those systems.

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

3.A: All forces share 3.A.1.1: The student is able 3.A.1: An observer in a particular reference certain common to express the motion of frame can describe the motion of an characteristics when an object using narrative, object using such quantities as position, considered by observers mathematical, and displacement, distance, velocity, speed, and in inertial reference graphical representations. acceleration. frames. [SP 1.5, 2.1, 2.2] a. Displacement, velocity, and acceleration 3.A.1.2: The student are all vector quantities. is able to design an b. Displacement is change in position. experimental investigation Velocity is the rate of change of position with of the motion of an object. time. Acceleration is the rate of change of [SP 4.2] velocity with time. Changes in each property 3.A.1.3: The student are expressed by subtracting initial values is able to analyze from final values. experimental data Relevant Equations: describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations. c. A choice of reference frame determines the [SP 5.1] direction and the magnitude of each of these quantities. d. There are three fundamental interactions or forces in nature: the gravitational force, the electroweak force, and the strong force. The fundamental forces determine both the structure of objects and the motion of objects. e. In inertial reference frames, forces are detected by their influence on the motion (specifically the velocity) of an object. So force, like velocity, is a vector quantity. A force vector has magnitude and direction. When multiple forces are exerted on an object, the vector sum of these forces, referred to as the net force, causes a change in the motion of the object. The acceleration of the object is proportional to the net force.

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Return to Table of Contents Table to Return versus

Circular motion and projectile motion are both are motion motion and projectile Circular motion will be discussed included. Circular in this document. later can be 4.A.1: The linear motion of a system and the displacement, velocity, described by of mass. of its center acceleration to the x, v, and a all refer a. The variables quantities. center-of-mass Equations: Relevant Essential Knowledge Essential students need to (What know) to apply only equations f. The kinematic Circular situations. constant acceleration both are motion motion and projectile in motion is further covered included. Circular equations kinematic three 3. The Area Content withdescribing linear motion constant are: dimensions two in one and acceleration analogous are motion there rotational For g. quantities such as angular position, angular The and angular acceleration. velocity, describing angular equations kinematic are: motion with constant angular acceleration Content Area 1: Kinematics 1: Kinematics Area Content

AP Physics 1: Algebra-Based AP Physics

4.A.1.1 The student to use is able of the representations of mass of an center system two-object isolated the motion of to analyze qualitatively the system and semiquantitatively. [SP 1.2, 1.4, 2.3, 6.4] Learning Objectives Learning students must be(What to do) able . Course and Exam Description and Exam Course The acceleration of 4.A: The acceleration of mass of a the center to the is related system on the exerted net force where system, All forces share share 3.A: All forces certain common characteristics by when considered in inertial observers frames. reference (Continued) Enduring Understanding Enduring concepts that (Core retain) students should 17 Content Outline Content Area 1: Kinematics

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

4.A: The acceleration of 4.A.2.1: The student is 4.A.2: The acceleration is equal to the rate of ramework the center of mass of a able to make predictions change of velocity with time, and velocity is F system is related to the about the motion of a equal to the rate of change of position with net force exerted on the ! system based on the fact time. F that acceleration is equal ! ∑ a. The acceleration of the center of mass of a Course Course system, where a = . m to the change in velocity system is directly proportional to the net force per unit time, and velocity (Continued) exerted on it by all objects interacting with the is equal to the change in system and inversely proportional to the mass position per unit time. of the system. [SP 6.4] b. Force and acceleration are both vectors, 4.A.2.3: The student with acceleration in the same direction as the is able to create net force. mathematical models and analyze graphical c. The acceleration of the center of mass of relationships for a system is equal to the rate of change of the acceleration, velocity, center of mass velocity with time, and the and position of the center center of mass velocity is equal to the rate of of mass of a system and change of the position of the center of mass use them to calculate with time. properties of the motion d. The variables x, v, and a all refer to the of the center of mass of a center-of-mass quantities. system. [SP 1.4, 2.2] Relevant Equations:   F a = m system "! ! Δx v avg = Δt ! ! Δv a avg = Δt

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Table of Contents Table

Return to Table of Contents Table to Return Systems have properties properties have Systems Essential Knowledge students need to (What know) is an object or a collection 1.A.1: A system no as having treated Objects are of objects. structure. internal in which internal of particles a. A collection all, or or not at little change interactions are in these interactions in which changes can be to the question addressed, irrelevant as an object. treated fundamental are particles Some elementary b. and Protons electrons). (e.g., particles of fundamental composed are neutrons as quarks) and might be treated (i.e., particles depending on the or objects, either systems question being addressed. and on neutrons charges c. The electric their quark compositions. from result protons 1.A.5: and the properties by determined of their constituent atomic interactions In AP Physics, substructures. and molecular of thewhen the constituent properties not important in modeling the parts are system, of the macroscopic behavior to as be referred itself may the system an object. of an Inertial mass is the property 1.C.1: its how that determines object or a system with other when it interacts motion changes objects or systems. a. Content Area 2: Dynamics 2: Dynamics Area Content AP Physics 1: Algebra-Based AP Physics

Learning Objectives students must be(What to do) able [While there is no specific [While there for learning objective it, EK 1.A.1 serves as other for a foundation in the learning objectives course.] 1.A.5.1: The student is or to model verbally able theproperties visually based on its of a system and to relate substructure in thethis to changes over properties system time as external variables [SP 1.1, 7.1] changed. are The student 1.C.1.1: to design an is able collecting experiment for the to determine data the between relationship on an exerted net force object its inertial mass and its acceleration. [SP 4.2] Objects and systems have properties systems have Objects as mass and and such structure. Systems internal may have charge. space explain be can used existing in Fields to interactions. be objects can other with object an of The interactions described by forces. in between changes in systems result can Interactions systems. those

Course and Exam Description and Exam Course Big Idea 4: Big Enduring Understanding concepts that (Core retain) students should Big Idea 2:Big Idea 3: Big structure 1.A: The internal determines of a system of the properties many system. Objects and 1.C: properties have systems of inertial mass and mass that are gravitational verified experimentally to be the same and that conservation satisfy principles. Content Area Dynamics 2: Idea 1: Big 19 Content Outline Content Area 2: Dynamics

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

1.C: Objects and 1.C.3.1: The student is 1.C.3: Objects and systems have properties ramework systems have properties able to design a plan for of inertial mass and gravitational mass that F of inertial mass and collecting data to measure are experimentally verified to be the same and gravitational mass that gravitational mass and to that satisfy conservation principles. are experimentally measure inertial mass and Course Course verified to be the to distinguish between the same and that satisfy two experiments. [SP 4.2] conservation principles. (Continued)

2.B: A gravitational field 2.B.1.1: The student is 2.B.1: A gravitational field at the location of is caused by an object able to apply to an object with mass m causes a gravitational with mass. calculate the gravitational force of magnitude mg to be exerted on the force on an object with object in the direction of the field. mass m in a gravitational a. On Earth, this gravitational force is called field of strength g in the weight. context of the effects of a net force on objects and b. The gravitational field at a point in space is systems. [SP 2.2, 7.2] measured by dividing the gravitational force exerted by the field on a test object at that point by the mass of the test object and has the same direction as the force. c. If the gravitational force is the only force exerted on the object, the observed free-fall acceleration of the object (in meters per second squared) is numerically equal to the magnitude of the gravitational field (in Newtons/kilogram) at that location. Relevant Equation:

3.A: All forces share 3.A.2.1: The student 3.A.2: Forces are described by vectors. certain common is able to represent a. Forces are detected by their influence on the characteristics when forces in diagrams or motion of an object. considered by observers mathematically using in inertial reference appropriately labeled b. Forces have magnitude and direction. frames. vectors with magnitude, direction, and units during the analysis of a situation. [SP 1.1]

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Return to Table of Contents Table to Return Essential Knowledge Essential students need to (What know) A force exerted on an object is always is always on an object exerted 3.A.3: A force of that object with due to the interaction another object. on itself. a force a. An object cannot exert there though rest, is at an object Even b. other on that object by exerted be forces may objects. an object, but not of c. The acceleration in the is always its velocity, necessarily on the object exerted of the net force direction other objects. by If one object exerts a force on a second on a force 3.A.4: If one object exerts a force exerts object, the second object always object in of equal magnitude on thethe first direction. opposite Content Area 2: Dynamics 2: Dynamics Area Content AP Physics 1: Algebra-Based AP Physics

Learning Objectives Learning students must be(What to do) able 3.A.3.1: The student a to analyze is able claims scenario and make arguments, (develop assertions) about justify on an exerted the forces other for objects object by or forces types of different components of forces. [SP 6.4, 7.2] 3.A.3.2: The student is a claim to challenge able athat an object can exert on itself. [SP 6.1] force 3.A.3.3: The student is to describe a force able between as an interaction objects and identifytwo force. any both objects for [SP 1.4] 3.A.4.1: The student to construct is able of physical explanations the involving situations bodies of interaction law third using Newton’s of and the representation of pairs action-reaction [SP 1.4, 6.2] forces. 3.A.4.2: The student is third to use Newton’s able claims and to make law about the predictions of pairs action-reaction objects when two forces interact. [SP 6.4, 7.2] 3.A.4.3: The student is situations to analyze able interactions involving objects among several using free-body by that include the diagrams of Newton’s application to identify law third [SP 1.4] forces. Course and Exam Description and Exam Course All forces share share 3.A: All forces certain common characteristics by when considered in inertial observers frames. reference (Continued) Enduring Understanding Enduring concepts that (Core retain) students should 21 Content Outline Content Area 2: Dynamics

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

3.B: Classically, the 3.B.1.1: The student is 3.B.1: If an object of interest interacts with ramework acceleration of an object able to predict the motion several other objects, the net force is the F interacting with other of an object subject vector sum of the individual forces. Projectile objects can be predicted to forces exerted by motion and circular motion are both included several objects using an in AP Physics 1. Course Course by using . application of Newton’s Relevant Equation: second law in a variety of physical situations with acceleration in one dimension. [SP 6.4, 7.2] 3.B.1.2: The student is Boundary Statement: able to design a plan AP Physics 2 contains learning objectives for to collect and analyze Enduring Understanding 3.B that focus on data for motion (static, electric and magnetic forces and other forces constant, or accelerating) arising in the context of interactions introduced from force measurements in Physics 2, rather than the mechanical and carry out an systems introduced in Physics 1. analysis to determine the relationship between the net force and the vector sum of the individual forces. [SP 4.2, 5.1] 3.B.1.3: The student is able to reexpress a free-body diagram representation into a mathematical representation and solve the mathematical representation for the acceleration of the object. [SP 1.5, 2.2]

3.B.2.1: The student is 3.B.2: Free-body diagrams are useful tools able to create and use free- for visualizing forces being exerted on a body diagrams to analyze single object and writing the equations that physical situations to represent a physical situation. solve problems with a. An object can be drawn as if it was motion qualitatively and extracted from its environment and the quantitatively. [SP 1.1, interactions with the environment identified. 1.4, 2.2] b. A force exerted on an object can be represented as an arrow whose length represents the magnitude of the force and whose direction shows the direction of the force. c. A coordinate system with one axis parallel to the direction of the acceleration simplifies the translation from the free body diagram to the algebraic representation. d. Free-body diagrams are depicted where the forces exerted on an object are represented as arrows pointing outward from a dot, and also diagrams that show at what point on the object each force is exerted.

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Return to Table of Contents Table to Return b. Force and acceleration are both vectors, both vectors, are and acceleration Force b. as the in the direction same with acceleration net force. Equations: Relevant Essential Knowledge Essential students need to (What know) the interaction from result Contact forces 3.C.4: anotherof one object touching object and they These forces. electric interatomic arise from friction, normal, spring include tension, forces 2). (Physics 1), and buoyant (Physics Equations: Relevant can be 4.A.1: The linear motion of a system and the displacement, velocity, described by of mass. of its center acceleration to the x, v, and a; all refer The variables quantities. center-of-mass Equation: Relevant The acceleration is equal to the rate of is equal to the rate 4.A.2: The acceleration is with time, and velocity of velocity change of position with of change equal to the rate time. of mass of a of the center a. The acceleration to the net force proportional is directly system with the interacting all objects on it by exerted to the mass proportional and inversely system of the system. Equation: Relevant Content Area 2: Dynamics 2: Dynamics Area Content The student is AP Physics 1: Algebra-Based AP Physics

4.A.2.2: 4.A.1.1 The student to use is able of the representations of mass of an center system two-object isolated the motion of to analyze qualitatively the system and semiquantitatively. [SP 1.2, 1.4, 2.3, 6.4] Learning Objectives Learning students must be(What to do) able The student is 3.C.4.1: claims about to make able contact forces various objects based on between cause of the microscopic [SP 6.1] those forces. The student is 3.C.4.2: to explain contact able friction, (tension, forces normal, buoyant, spring) as arising from forces electric interatomic and that they therefore certain directions. have [SP 6.2] able to evaluate using to evaluate able whether data all given on a system the forces or whether all the parts been have of a system identified. [SP 5.3] . The acceleration of The acceleration : At the macroscopic the macroscopic : At Course and Exam Description and Exam Course 4.A: 3.C can be forces level, as either categorized (action-at-a- long-range or contact distance) forces forces. Enduring Understanding Enduring concepts that (Core retain) students should the center of mass of a the center to the is related system on the exerted net force where system, 23 Content Outline Content Area 2: Dynamics

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

4.A: The acceleration of c. The acceleration of the center of mass of ramework the center of mass of a a system is equal to the rate of change of the F system is related to the center of mass velocity with time, and the net force exerted on the center of mass velocity is equal to the rate of system, where . change of the position of the center of mass Course Course with time. (Continued) d. The variables x, v, and a all refer to the center-of-mass quantities. Relevant Equation:

4.A.3.1: The student is 4.A.3: Forces that that systems exert on each able to apply Newton’s other are due to interactions between objects second law to systems in the systems. If the interacting objects are to calculate the change parts of the same system, there will be no in the center-of-mass change in the center-of-mass velocity of that velocity when an external system. force is exerted on the Relevant Equation: system. [SP 2.2] 4.A.3.2: The student is able to use visual or mathematical representations of the forces between objects in a system to predict whether or not there will be a change in the center- of-mass velocity of that system. [SP 1.4]

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Return to Table of Contents Table to Return Boundary Statement: fields; Physics 2 Physics 1 treats gravitational treats and magnetic fields. electric Essential Knowledge students need to (What know) of mass is the property : Gravitational 1.C.2 the that determines an object or a system with interaction of the gravitational strength fields. or gravitational systems, other objects, mass of an object a. The gravitational on the exerted the amount of force determines field. a gravitational object by all objects fall surface, the Earth’s Near b. with the same acceleration, (in a vacuum) of their inertial mass. regardless properties have Objects and systems 1.C.3: mass that of inertial and gravitational mass to be the same and verified experimentally are principles. conservation that satisfy as a function of gives, field 2.A.1: A vector of a position (and perhaps time), the value a vector. quantity that is described by physical vectors by field represented are fields a. Vector and magnitude. direction indicating object with than one source When more b. the field is present, charge mass or electric addition. vector by can be determined value can be field vector a known c. Conversely, about the number, inferences used to make of sources. size, and location relative Content Area 3: Circular Motion and Gravitation and Gravitation Motion 3: Circular Area Content AP Physics 1: Algebra-Based AP Physics

Learning Objectives students must be(What to do) able [While there is no specific [While there for learning objective serves as it, EK 1.C.2 other for a foundation in the learning objectives course.] The student is 1.C.3.1: for to design a plan able to measure data collecting mass and to gravitational inertial mass and measure the to distinguish between [SP 4.2] experiments. two is no specific [While there for learning objective it, EK 2.A.1 serves as other for a foundation in the learning objectives course.] Objects and systems have properties systems have Objects as mass and and such structure. Systems internal may have charge. space explain be can used existing in Fields to interactions. be objects can other with object an of The interactions described by forces. in between changes in systems result can Interactions systems. those

Course and Exam Description and Exam Course Big Idea 4: Big Enduring Understanding concepts that (Core retain) students should Big Idea 2:Big Idea 3: Big Objects and 1.C: properties have systems of inertial and mass mass that are gravitational verified experimentally to be the same and that conservation satisfy principles. a associates 2.A: A field of some physical value point quantity with every models in space. Field describing useful for are that occur interactions a distance (long-range at as a as well forces) of other physical variety phenomena. Content Area 3: Circular Motion and Gravitation Idea 1: Big 25 Content Outline Content Area 3: Circular Motion and Gravitation

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

2.B: A gravitational field 2.B.1.1: The student is 2.B.1: A gravitational field at the location of ramework is caused by an object able to apply to an object with mass m causes a gravitational F with mass. calculate the gravitational force of magnitude mg to be exerted on the force on an object with object in the direction of the field. mass m in a gravitational

Course Course a. On Earth, this gravitational force is called field of strength g in the weight. context of the effects of a net force on objects and b. The gravitational field at a point in space is systems. [SP 2.2, 7.2] measured by dividing the gravitational force exerted by the field on a test object at that point by the mass of the test object and has the same direction as the force. c. If the gravitational force is the only force exerted on the object, the observed free-fall acceleration of the object (in meters per second squared) is numerically equal to the magnitude of the gravitational field (in Newtons/kilogram) at that location. Relevant Equation:

2.B.2.1: The student is 2.B.2: The gravitational field caused by a able to apply to spherically symmetric object with mass is radial and, outside the object, varies as the calculate the gravitational inverse square of the radial distance from the field due to an object with center of that object. mass M, where the field is a vector directed toward a. The gravitational field caused by a the center of the object of spherically symmetric object is a vector mass M. [SP 2.2] whose magnitude outside the object is equal 2.B.2.2: The student is to . able to approximate a b. Only spherically symmetric objects will numerical value of the be considered as sources of the gravitational gravitational field (g) near field. the surface of an object Relevant Equation: from its radius and mass relative to those of the Earth or other reference objects. [SP 2.2]

3.A: All forces share 3.A.1.1: The student 3.A.1: An observer in a particular reference certain common is able to express the frame can describe the motion of an object characteristics when motion of an object using using such quantities as position, displacement, considered by observers narrative, mathematical, distance, velocity, speed, and acceleration. in inertial reference and graphical a. Displacement, velocity, and acceleration are frames. representations. all vector quantities. [SP 1.5, 2.1, 2.2] b. Displacement is change in position. Velocity is the rate of change of position with time. Acceleration is the rate of change of velocity with time. Changes in each property are expressed by subtracting initial values from final values.

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Return to Table of Contents Table to Return versus g. The kinematic equations only apply to apply only equations The kinematic g. Circular situations. constant acceleration both motion are motion and projectile will be discussed motion included. Circular in this document. later analogous are motion, there rotational h. For quantities such as angular position, angular and angular acceleration. velocity, Equations: Relevant Essential Knowledge Essential students need to (What know) Equations: Relevant the determines frame c. A choice of reference and the magnitude of each of these direction quantities. fundamental interactions of three know d. We force, the gravitational in nature: or forces force. and the strong force, the electroweak both the determine The fundamental forces of objects and the motion of objects. structure are forces frames, e. In inertial reference their on influence by the motion detected of an object. So velocity) the (specifically A force quantity. is a vector velocity, like force, When and direction. has magnitude vector on an object, the exerted are forces multiple to as the referred sum of these forces, vector in the motion of causes a change net force, of the object is the object. The acceleration to the net force. proportional apply only equations kinematic f. The three Circular situations. to constant acceleration both motion are motion and projectile in motion is further covered included. Circular equations kinematic 3. The three Area Content describing linear motion with constant dimensions are: in one and two acceleration The student Content Area 3: Circular Motion and Gravitation and Gravitation Motion 3: Circular Area Content AP Physics 1: Algebra-Based AP Physics

Learning Objectives Learning students must be(What to do) able 3.A.1.2: The student to design an is able experimental investigation of the an object. motion of [SP 4.2] 3.A.1.3: to analyze is able experimental data describing the motion of to an object and is able of the the results express using narrative, analysis andmathematical representatives. graphical [SP 5.1] Course and Exam Description and Exam Course All forces share share 3.A: All forces certain common characteristics by when considered in inertial observers frames. reference (Continued) Enduring Understanding Enduring concepts that (Core retain) students should 27 Content Outline Content Area 3: Circular Motion and Gravitation

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

3.A: All forces share i. This also includes situations where there is ramework certain common both a radial and tangential acceleration for F characteristics an object moving in a circular path. when considered by observers in inertial Relevant Equation:

Course Course reference frames. (Continued)

Boundary Statement: AP Physics 2 has learning objectives under Enduring Understanding 3.A that focus on electric and magnetic forces and other forces arising in the context of interactions introduced in Physics 2, rather than the mechanical systems introduced in Physics 1.

3.A.2.1: The student is 3.A.2: Forces are described by vectors. able to represent forces in a. Forces are detected by their influence on the diagrams or mathematically motion of an object. using appropriately labeled vectors with magnitude, b. Forces have magnitude and direction. direction, and units during the analysis of a situation. [SP 1.1]

3.A.3.1: The student 3.A.3: A force exerted on an object is always is able to analyze a due to the interaction of that object with another scenario and make claims object. (develop arguments, a. An object cannot exert a force on itself. justify assertions) about the forces exerted on an b. Even though an object is at rest, there may be object by other objects for forces exerted on that object by other objects. different types of forces or c. The acceleration of an object, but not components of forces. necessarily its velocity, is always in the direction [SP 6.4, 7.2] of the net force exerted on the object by other 3.A.3.3: The student is objects. able to describe a force as an interaction between two objects and identify both objects for any force. [SP 1.4]

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Return to Table of Contents Table to Return Boundary Statement: under learning objectives AP Physics 2 contains on 3.B that focus Enduring Understanding and other forces and magnetic forces electric introduced of interactions arising in the context than the mechanical in Physics 2, rather in Physics 1. introduced systems Essential Knowledge Essential students need to (What know) If one object exerts a force on a second a force 3.A.4: If one object exerts a force exerts object, the object always second object in theof equal magnitude on the first direction. opposite with interacts If an object of interest 3.B.1: is the the other net force objects, several forces. sum of the individual vector

Content Area 3: Circular Motion and Gravitation and Gravitation Motion 3: Circular Area Content AP Physics 1: Algebra-Based AP Physics

The student is 3.B.1.2: to design a plan able and analyze to collect motion (static, for data constant, or accelerating) measurements force from and carry out an the to determine analysis the between relationship and the vector net force sum of the individual [SP 4.2, 5.1] forces. The student 3.B.1.3: to reexpress is able diagram a free-body into representation a mathematical and representation the mathematical solve the for representation of the object. acceleration Learning Objectives Learning students must be(What to do) able 3.A.4.1: The student is able to construct explanations situations of physical of the interaction involving third bodies using Newton’s and the representation law of pairs of action-reaction [SP 1.4, 6.2] forces. 3.A.4.2: The student is able to law third to use Newton’s and predictions claims make about the action-reaction when two of forces pairs [SP 6.4, 7.2] objects interact. 3.A.4.3: The student is situations to analyze able interactions involving objects by among several diagrams using free-body that include the application to law third of Newton’s [SP 1.4] identify forces. [SP 1.5, 2.2] . Course and Exam Description and Exam Course All forces share certain share 3.A: All forces common characteristics by when considered in inertial observers frames. reference (Continued) Enduring Understanding Enduring concepts that (Core retain) students should : Classically, the 3.B: Classically, of an object acceleration with other interacting objects can be predicted using by 29 Content Outline Content Area 3: Circular Motion and Gravitation

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

3.B: Classically, the 3.B.2.1: The student is 3.B.2: Free-body diagrams are useful tools ramework acceleration of an object able to create and use free- for visualizing forces being exerted on a F interacting with other body diagrams to analyze single object and writing the equations that objects can be predicted physical situations to represent a physical situation. solve problems with a. An object can be drawn as if it was Course Course by using . motion qualitatively and extracted from its environment and the quantitatively. [SP 1.1, (Continued) interactions with the environment identified. 1.4, 2.2] b. A force exerted on an object can be represented as an arrow whose length represents the magnitude of the force and whose direction shows the direction of the force. c. A coordinate system with one axis parallel to the direction of the acceleration simplifies the translation from the free body diagram to the algebraic representation.

3.C: At the macroscopic 3.C.1.1: The student is 3.C.1: Gravitational force describes the level, forces can be able to use Newton’s law interaction of one object with mass with categorized as either of gravitation to calculate another object with mass. long-range (action-at-a- the gravitational force the a. The gravitational force is always attractive. distance) forces or contact two objects exert on each forces. other and use that force in b. The magnitude of force between two contexts other than orbital spherically symmetric objects of mass m1 and motion. [SP 2.2] m is where r is the center-to-center 3.C.1.2: The student is 2 able to use Newton’s law distance between the objects. of gravitation to calculate c. In a narrow range of heights above the the gravitational force Earth’s surface, the local gravitational field, g, between two objects and is approximately constant. use that force in contexts involving orbital motion Relevant Equations: (for circular orbital motion only in Physics 1). [SP 2.2]

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Return to Table of Contents Table to Return The acceleration is equal to the rate of is equal to the rate 4.A.2: The acceleration is with time, and velocity of velocity change of position with of change equal to the rate time. of mass of a of the center a. The acceleration to the net force proportional is directly system with the all objects interacting on it by exerted to the mass proportional and inversely system of the system. both vectors, are and acceleration Force b. as the in the direction same with acceleration net force. Equation: Relevant Essential Knowledge Essential students need to (What know) the from results force Electric 3.C.2: of one object that has an electric interaction with another object that an electric has charge charge. the properties dominate forces a. Electric experiences. of the our everyday objects in of particle number the large However, more it that make occur interactions of in terms forces everyday to treat convenient contact forces, called nonfundamental forces friction, and tension. such as normal force, or be attractive may forces Electric b. on the depending upon the charges repulsive, objects involved. Equations: Relevant Gravitational forces are exerted at all at exerted are forces Gravitational 3.G.1: distance the at largest and dominate scales and mass scales.

[SP 7.1] Content Area 3: Circular Motion and Gravitation and Gravitation Motion 3: Circular Area Content AP Physics 1: Algebra-Based AP Physics

4.A.2.2: The student is using to evaluate able whether data all given on a system the forces or whether all the parts been have of a system identified. [SP 5.3] Learning Objectives Learning students must be(What to do) able The student 3.C.2.2: to connect theis able concepts of gravitational to force and electric force similarities and compare the between differences [SP 7.2] forces. The student is 3.G.1.1: situations to articulate able when the gravitational is the dominant force and when the force weak, electromagnetic, can be forces and strong ignored. . Certain of types Course and Exam Description and Exam Course 3.G: At the macroscopic the macroscopic At 3.C: can be forces level, as either categorized (action- long-range forces at-a-distance) or contact forces. (Continued) Enduring Understanding Enduring concepts that (Core retain) students should forces are considered considered are forces fundamental. The acceleration of 4.A: The acceleration of mass of a the center to the is related system on the exerted net force where system, 31 Content Outline Content Area 4: Energy

Content Area 4: Energy Big Idea 3: The interactions of an object with other objects can be described by forces. ramework F Big Idea 4: Interactions between systems can result in changes in those systems. Course Course Big Idea 5: Changes that occur as a result of interactions are constrained by conservation laws.

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

3.E: A force exerted on 3.E.1.1: The student is 3.E.1: The change in the kinetic energy of an an object can change able to make predictions object depends on the force exerted on the the kinetic energy of the about the changes in object and on the displacement of the object object. kinetic energy of an object during the interval that the force is exerted. based on considerations a. Only the component of the net force exerted of the direction of the net on an object parallel or antiparallel to the force on the object as the displacement of the object will increase object moves. [SP 6.4, 7.2] (parallel) or decrease (antiparallel) the kinetic 3.E.1.2: The student energy of the object. is able to use net force b. The magnitude of the change in the kinetic and velocity vectors to energy is the product of the magnitude of the determine qualitatively displacement and of the magnitude of the whether kinetic energy of component of force parallel or antiparallel to the an object would increase, displacement. decrease, or remain unchanged. [SP 1.4] Relevant Equation: 3.E.1.3: The student is able to use force c. The component of the net force exerted on and velocity vectors to an object perpendicular to the direction of the determine qualitatively displacement of the object can change the or quantitatively the net direction of the motion of the object without force exerted on an object changing the kinetic energy of the object. This and qualitatively whether should include uniform circular motion and kinetic energy of that projectile motion. object would increase, decrease, or remain d. The kinetic energy of a rigid system may unchanged. [SP 1.4, 2.2] be translational, rotational, or a combination of both. The change in the rotational kinetic 3.E.1.4: The student is energy of a rigid system is the product of the able to apply mathematical angular displacement and the net torque. routines to determine the change in kinetic energy Relevant Equations: of an object given the forces on the object and the displacement of the object. [SP 2.2]

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Return to Table of Contents Table to Return

Mechanical energy (the sum of kineticMechanical energy Content Area 4: Energy 4: Energy Area Content b. Work (change in energy) can be found from from can be found in energy) (change Work b. of the magnitude of the under a graph the area to the displacement component parallel force displacement. versus Equation: Relevant Essential Knowledge Essential students need to (What know) includes of a system The energy 4.C.1: and energy, potential its kinetic energy, include Examples energy. internal microscopic elastic potential energy, potential gravitational and kinetic energy. energy, to be considered may rigid body a. A rotating, both translational have and may be a system, kinetic energy. and rotational Although is not part of thermodynamics b. 1, included is the idea that during an Physics of theinelastic collision, some mechanical to) thermal as (converts dissipates energy energy. Equations: Relevant 4.C.2: into or out is transferred energy) and potential is exerted force when an external of a system such that a component of the force on a system The process to its displacement. is parallel is is transferred which the energy through work. called during a given is constant a. If the force displacement, then the done is work of the displacement and thethe product or antiparallel parallel component of the force to the displacement. Equation: Relevant The student is AP Physics 1: Algebra-Based AP Physics

4.C.2.1: Learning Objectives Learning be students must (What to do) able The student is 4.C.1.1: the total to calculate able and of a system energy the mathematical justify used in the routines of component calculation within types of energy whose sum is the system [SP 1.4, the total energy. 2.1, 2.2] The student is 4.C.1.2: changes to predict able of a in the total energy due to changes system in position and speed of objects or frictional within the interactions [SP 6.4] system. able to make predictions predictions to make able in theabout the changes of a mechanical energy when a component system acts force of an external or antiparallel parallel of the to the direction displacement of the center [SP 6.4] of mass. The student is 4.C.2.2: the concepts to apply able of Energy of Conservation and the Work-Energy to determine theorem and/or qualitatively that work quantitatively done on a two-object in linear motion system the kinetic will change of the center energy of mass of the system, of energy the potential and/or the the systems, of the energy internal [SP 1.4, 2.2, 7.2] system. Course and Exam Description and Exam Course Interactions with Interactions 4.C: other systems objects or the total can change of a system. energy Enduring Understanding Enduring concepts that (Core retain) students should 33 Content Outline Content Area 4: Energy

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

5.A: Certain quantities [While there is no specific 5.A.1: A system is an object or a collection of ramework are conserved, in the learning objective for objects. The objects are treated as having no F sense that the changes it, EK 5.A.1 serves as internal structure. of those quantities in a a foundation for other given system are always learning objectives in the Course Course equal to the transfer of course.] that quantity to or from the system by all possible 5.A.2.1: The student 5.A.2: For all systems under all interactions with other is able to define open circumstances, energy, charge, linear systems. and closed systems momentum, and angular momentum are for everyday situations conserved. For an isolated or a closed system, and apply conservation conserved quantities are constant. An open concepts for energy, system is one that exchanges any conserved charge, and linear quantity with its surroundings. momentum to those situations. [SP 6.4, 7.2]

[While there is no specific 5.A.3: An interaction can be either a force learning objective for exerted by objects outside the system or the it, EK 5.A.3 serves as transfer of some quantity with objects outside a foundation for other the system. learning objectives in the course.]

[While there is no specific 5.A.4: The placement of a boundary between learning objective for a system and its environment is a decision it, EK 5.A.4 serves as made by the person considering the situation a foundation for other in order to simplify or otherwise assist in learning objectives in the analysis. course.]

5.B: The energy of a 5.B.1.1: The student is able 5.B.1: Classically, an object can only have system is conserved. to set up a representation kinetic energy since potential energy requires or model showing that an interaction between two or more objects. a single object can only Relevant Equation: have kinetic energy and use information about that object to calculate its kinetic energy. [SP 1.4, 2.2] 5.B.1.2: The student is Boundary Statement: able to translate between Conservation principles apply in the context a representation of a of the appropriate Physics 1 and Physics 2 single object, which courses. Work, potential energy, and kinetic can only have kinetic energy concepts are related to mechanical energy, and a system that systems in Physics 1 and electric, magnetic, includes the object, which thermal, and atomic and elementary particle may have both kinetic systems in Physics 2. and potential energies. [SP 1.5]

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Return to Table of Contents Table to Return The internal energy of a system of a system energy The internal Content Area 4: Energy 4: Energy Area Content Essential Knowledge Essential students need to (What know) structure with internal A system 5.B.2: in and changes energy, internal can have in can result structure internal a system’s 1: . [Physics energy in internal changes and simple oscillators includes mass-spring 2: includes charged Physics pendulums. and examining fields objects in electric in with changes energy in internal changes configuration.] A system with internal structure can structure with internal A system 5.B.3: exists energy Potential energy. potential have if the objects withinwithin that a system forces. with conservative interact system force a conservative done by a. The work The work is independent of the path taken. to the external forces description is used for is used when the energy Potential system. parts between interactions internal are forces of the system. can result structure in the internal Changes b. Examples energy. in potential in changes falling objects include mass-spring oscillators, field. in a gravitational in a circuit potential in electric c. The change per unit energy in potential is the change of in the context 1: only [Physics charge. circuits.] Equations: Relevant 5.B.4: 5.B.4: of theincludes the objects that kinetic energy energy and the potential up the system make of the objects make of thethat configuration up the system. system, is constant in a closed a. Since energy can energy potential in a system’s changes kinetic to the system’s in changes result energy. and kinetic in potential The changes b. be further may in a system energies the construction of the by system. constrained

[SP 1.4, 2.1, 2.2] The student AP Physics 1: Algebra-Based AP Physics

5.B.4.1: Learning Objectives Learning be students must (What to do) able The student 5.B.2.1: the to calculate is able of a behavior expected the using object system ignoring by model (i.e., in internal changes a to analyze structure) when the Then, situation. the student model fails, theof use can justify of energy conservation to calculate principles in internal the change in due to changes energy because structure internal a the object is actually [SP 1.4, 2.1] system. The student 5.B.3.1: to describe and is able and/or qualitative make predictions quantitative examples about everyday with internal of systems energy. potential [SP 2.2, 6.4, 7.2] The student is 5.B.3.2: quantitative to make able of thecalculations internal of a energy potential a description from system of that system. or diagram [SP 1.4, 2.2] The student 5.B.3.3: to apply is able reasoning mathematical a description to create potential of the internal of a system energy a description or from of the objects diagram in that and interactions [SP 1.4, 2.2] system. is able to describe and is able about predictions make of energy the internal [SP 6.4, 7.2] systems. The student is 5.B.4.2: changes to calculate able and in kinetic energy of a energy potential using information system, of that representations from system. Course and Exam Description and Exam Course The energy of a The energy 5.B: is conserved. system (Continued) Enduring Understanding Enduring concepts that (Core retain) students should 35 Content Outline Content Area 4: Energy

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

5.B: The energy of a 5.B.5.1: The student 5.B.5: Energy can be transferred by an ramework system is conserved. is able to design an external force exerted on an object or system F experiment and analyze that moves the object or system through a (Continued) data to examine how a distance; this energy transfer is called work. force exerted on an object Energy transfer in mechanical or electrical Course Course or system does work on systems may occur at different rates. Power the object or system as it is defined as the rate of energy transfer into, moves through a distance. out of, or within a system. [A piston filled with [SP 4.2, 5.1] gas getting compressed or expanded is treated 5.B.5.2: The student in Physics 2 as part of thermodynamics.] is able to design an Relevant Equations: experiment and analyze graphical data in which interpretations of the area under a force-distance curve are needed to determine the work done on or by the object or system. [SP 4.2, 5.1] 5.B.5.3: The student is able to predict and calculate from graphical data the energy transfer to or work done on an object or system from information about a force exerted on the object or system through a distance. [SP 1.4, 2.2, 6.4] 5.B.5.4: The student is able to make claims about the interaction between a system and its environment in which the environment exerts a force on the system, thus doing work on the system and changing the energy of the system (kinetic energy plus potential energy). [SP 6.4, 7.2] 5.B.5.5: The student is able to predict and calculate the energy transfer to (i.e., the work done on) an object or system from information about a force exerted on the object or system through a distance. [SP 2.2, 6.4]

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Return to Table of Contents Table to Return Content Area 4: Energy 4: Energy Area Content Essential Knowledge Essential students need to (What know) In a collision between objects, linear objects, In a collision between 5.D.1: In an elastic momentum is conserved. is the same before collision, kinetic energy and after. the linear momentum is system, a. In a closed the collision. constant throughout after the kinetic energy system, a closed In b. thean elastic collision is same as the kinetic the collision. before energy Equations: Relevant

The student AP Physics 1: Algebra-Based AP Physics

Learning Objectives Learning be students must (What to do) able The student is 5.D.1.1: qualitative to make able about predictions phenomena natural based on conservation of linear momentum of and restoration in elastic kinetic energy [SP 6.4, 7.2] collisions. 5.D.1.2: the to apply is able of conservation principles of momentum and of kinetic restoration a to reconcile energy to that appears situation and elastic, be isolated indicate but in which data that linear momentum are and kinetic energy thenot the same after refining by interaction, a scientific question to that identify interactions not been considered. have Students will be expected and/ qualitatively to solve one- for or quantitatively anddimensional situations in two- qualitatively only dimensional situations. [SP 2.2, 3.2, 5.1, 5.3] The student 5.D.1.3: to apply is able routines mathematical to appropriately involving problems elastic collisions in one dimension and justify the of those selection routines mathematical based on conservation of momentum and of kinetic restoration [SP 2.1, 2.2] energy. Course and Exam Description and Exam Course 5.D: The linear is momentum of a system conserved. Enduring Understanding Enduring concepts that (Core retain) students should 37 Content Outline Content Area 4: Energy

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

5.D: The linear 5.D.1.4: The student ramework momentum of a system is able to design an F is conserved. experimental test (Continued) of an application of the principle of the Course Course conservation of linear momentum, predict an outcome of the experiment using the principle, analyze data generated by that experiment whose uncertainties are expressed numerically, and evaluate the match between the prediction and the outcome. [SP 4.2, 5.1, 5.3, 6.4] 5.D.1.5: The student is able to classify a given collision situation as elastic or inelastic, justify the selection of conservation of linear momentum and restoration of kinetic energy as the appropriate principles for analyzing an elastic collision, solve for missing variables, and calculate their values. [SP 2.1, 2.2]

5.D.2.1: The student 5.D.2: In a collision between objects, linear is able to qualitatively momentum is conserved. In an inelastic predict, in terms of linear collision, kinetic energy is not the same before momentum and kinetic and after the collision. energy, how the outcome a. In a closed system, the linear momentum is of a collision between constant throughout the collision. two objects changes depending on whether b. In a closed system, the kinetic energy after the collision is elastic or an inelastic collision is different from the inelastic. [SP 6.4, 7.2] kinetic energy before the collision. 5.D.2.3: The student Relevant Equations: is able to apply the conservation of linear momentum to a closed system of objects involved in an inelastic collision to predict the change in kinetic energy. [SP 6.4, 7.2]

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Return to Table of Contents Table to Return Essential Knowledge need to students (What know) in momentum of an object The change 3.D.1: of the net force in the direction is a vector on the object. exerted Equation: Relevant The change in momentum of an object The change 3.D.2: a time interval. over occurs on a that one object exerts a. The force the of the momentum second object changes second object (in the absence of other forces on the second object). in momentum of that The change b. object depends on the impulse, which is and the force of the average the product during which the interaction time interval occurred. Equation: Relevant Content Area 5: Momentum 5: Momentum Area Content

The student is able The student is able The student is able AP Physics 1: Algebra-Based AP Physics

3.D.2.1: Learning Objectives must be students (What to do) able 3.D.1.1: the ofto justify selection needed to determine data the between the relationship acting of the force direction on an object and the change in momentum caused by [SP 4.1] that force. to justify the of selection to justify the calculation for routines of the relationships in changes between momentum of an object, impulse, and force, average [SP 2.1] time of interaction. The student is 3.D.2.2: the change to predict able in momentum of an object force the average from on the object and exerted of time during the interval exerted. is which the force [SP 6.4] The student is 3.D.2.3: to data to analyze able the change characterize in momentum of an object force the average from on the object and exerted of time during the interval is exerted. which the force [SP 5.1] The student is 3.D.2.4: to design a plan for able to investigate data collecting between the relationship in momentum andchanges on exerted force the average time. [SP 4.2] an object over The interactions of an object with other objects can be objects can other with object an of The interactions described by forces. systems. those in between changes in systems result can Interactions are interactions of occur as a result that Changes constrained by conservation laws.

dea 3: dea4: dea5: I I I Course and Exam Description and Exam Course Enduring Understanding that concepts (Core retain) students should Big Big on exerted 3.D: A force the an object can change momentum of the object. Content Area 5: Momentum 5: Area Content Big 39 Content Outline Content Area 5: Momentum

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

4.B: Interactions with 4.B.1.1: The student is able 4.B.1: The change in linear momentum for ramework other objects or systems to calculate the change in a constant-mass system is the product of F can change the total linear linear momentum of a two- the mass of the system and the change in momentum of a system. object system with constant velocity of the center of mass. mass in linear motion from

Course Course Relevant Equation: a representation of the system (data, graphs, etc.). [SP 1.4, 2.2] 4.B.1.2: The student is able to analyze data to find the change in linear momentum for a constant- mass system using the product of the mass and the change in velocity of the center of mass. [SP 5.1]

4.B.2.1: The student is 4.B.2: The change in linear momentum of able to apply mathematical the system is given by the product of the routines to calculate the average force on that system and the time change in momentum of interval during which the force is exerted. a system by analyzing the a. The units for momentum are the same as average force exerted over a the units of the area under the curve of a certain time on the system. force versus time graph. [SP 2.2] b. The change in linear momentum and force 4.B.2.2: The student is are both vectors in the same direction. able to perform analysis on data presented as a force- Relevant Equations: time graph and predict the change in momentum of a system. [SP 5.1]

5.A: Certain quantities 5.A.2.1: The student is 5.A.2: For all systems under all are conserved, in the able to define open and circumstances, energy, charge, linear sense that the changes closed systems for everyday momentum, and angular momentum are of those quantities in a situations and apply conserved. For an isolated or a closed given system are always conservation concepts system, conserved quantities are constant. equal to the transfer of for energy, charge, and An open system is one that exchanges any that quantity to or from linear momentum to those conserved quantity with its surroundings. the system by all possible situations. [SP 6.4, 7.2] interactions with other systems.

5.D: The linear 5.D.1.1: The student is 5.D.1: In a collision between objects, linear momentum of a system is able to make qualitative momentum is conserved. In an elastic conserved. predictions about natural collision, kinetic energy is the same before phenomena based on and after. conservation of linear a. In a closed system, the linear momentum momentum and restoration is constant throughout the collision. of kinetic energy in elastic collisions. [SP 6.4, 7.2] b. In a closed system, the kinetic energy after an elastic collision is the same as the kinetic energy before the collision.

Return to 40 AP Physics 1: Algebra-Based Course and Exam Description Return to TableTable of Contents of Contents

Return to Table of Contents Table to Return Boundary Statement: Boundary Statement: and Physics 1 includes a quantitative of conservation treatment qualitative and a of momentum in one dimension of conservation treatment semiquantitative items Test of momentum in two dimensions. equations of simultaneous involving solution items not included in Physics 1, but are whether students set up the testing can how about reason and can equations properly changing a given mass, speed, or angle would included. are other quantities affect Physics 1 includes only conceptual of mass motion of of center understanding of calculation the need for without a system of mass. center from includes topics The Physics 1 course of 5.D in the context Enduring Understanding systems. mechanical Essential Knowledge Essential students need to (What know) Relevant Equations: Relevant Content Area 5: Momentum 5: Momentum Area Content

The student AP Physics 1: Algebra-Based AP Physics

Learning Objectives Learning students must be(What to do) able The student is able 5.D.1.2: the of principles to apply of momentum conservation of kinetic and restoration a to reconcile energy to that appears situation and elastic, be isolated indicate but in which data thatlinear momentum are and kinetic energy thenot the same after refining by interaction, a scientific question to that identify interactions not been considered. have Students will be expected and/ qualitatively to solve one- for or quantitatively and dimensional situations in two- qualitatively only [SP dimensional situations. 2.2, 3.2, 5.1, 5.3] The student is 5.D.1.3: mathematical to apply able to appropriately routines elastic involving problems collisions in one dimension the selection and justify of those mathematical based on routines of momentum conservation of kinetic and restoration [SP 2.1, 2.2] energy. 5.D.1.4: to design anis able of an experimental test of theapplication principle of linear of the conservation an momentum, predict outcome of the experiment using the principle, by generated data analyze that experiment whose expressed uncertainties are evaluate and numerically, thethe between match and the outcome. prediction [SP 4.2, 5.1, 5.3, 6.4] Course and Exam Description and Exam Course 5.D: The linear momentum of a system is conserved. (Continued) Enduring Understanding Enduring concepts that (Core retain) students should 41 Content Outline Content Area 5: Momentum

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

5.D: The linear 5.D.1.5: The student is ramework momentum of a system able to classify a given F is conserved. collision situation as elastic (Continued) or inelastic, justify the selection of conservation Course Course of linear momentum and restoration of kinetic energy as the appropriate principles for analyzing an elastic collision, solve for missing variables, and calculate their values. [SP 2.1, 2.2]

5.D.2.1: The student is able 5.D.2: In a collision between objects, linear to qualitatively predict, in momentum is conserved. In an inelastic terms of linear momentum collision, kinetic energy is not the same and kinetic energy, how before and after the collision. the outcome of a collision a. In a closed system, the linear momentum between two objects is constant throughout the collision. changes depending on whether the collision is b. In a closed system, the kinetic energy elastic or inelastic. after an inelastic collision is different from [SP 6.4, 7.2] the kinetic energy before the collision. 5.D.2.2: The student is Relevant Equations: able to plan data collection strategies to test the law of conservation of momentum in a two-object collision that is elastic or inelastic and analyze the resulting data graphically. [SP 4.1, 4.2, 5.1] 5.D.2.3: The student is able to apply the conservation of linear momentum to a closed system of objects involved in an inelastic collision to predict the change in kinetic energy. [SP 6.4, 7.2] 5.D.2.4: The student is able to analyze data that verify conservation of momentum in collisions with and without an external friction force. [SP 4.1, 4.2, 4.4, 5.1, 5.3]

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Return to Table of Contents Table to Return Essential Knowledge Essential students need to (What know) of mass of the center The velocity 5.D.3: an by cannot be changed of the system 1: [Physics within the system. interaction of mass; of centers includes no calculations until Physics the is not provided equation without doing calculations, 2. However, to be expected 1 students are Physics of mass of highly the center to locate able such as a symmetric mass distributions, or density, or cube of uniform rod uniform of equal mass.] spheres two depends of mass of a system a. The center upon the masses and positions of the objects (a system In an isolated in the system. the velocity forces) with no external system of mass does not change. of the center collide, the When objects in a system b. of mass of the of the system center velocity is force an external unless will not change on the system. exerted 1 is the idea that c. Included in Physics and lighter is both a heavier there where to of mass is closer the center mass, a qualitative Only mass. the heavier of this concept is required. understanding Content Area 5: Momentum 5: Momentum Area Content

AP Physics 1: Algebra-Based AP Physics

Learning Objectives Learning students must be(What to do) able The student is 5.D.2.5: to classify a given able as elastic collision situation the or inelastic, justify of conservation selection of linear momentum as solution the appropriate inelastic an method for that collision, recognize is a common final there the colliding for velocity objects in the totally for inelastic case, solve and missing variables, . [SP their values calculate 2.1, 2.2] The student is able 5.D.3.1: of the the velocity to predict of mass of a system center is no interaction when there but outside of the system is an interaction there the (i.e., within the system recognizes student simply within a that interactions the do not affect system of mass motion of center to and is able the system is no that there determine [SP 6.4] force). external Course and Exam Description and Exam Course 5.D: The linear momentum of a system is conserved. (Continued) Enduring Understanding Enduring concepts that (Core retain) students should 43 Content Outline Content Area 6: Simple Harmonic Motion

Content Area 6: Simple Harmonic Motion Big Idea 3: The interactions of an object with other objects can be described by forces. ramework F Big Idea 5: Changes that occur as a result of interactions are constrained by conservation laws. Course Course Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

3.B: Classically, the 3.B.3.1: The student is 3.B.3: Restoring forces can result in acceleration of an object able to predict which oscillatory motion. When a linear restoring interacting with other properties determine force is exerted on an object displaced from an objects can be predicted the motion of a simple equilibrium position, the object will undergo a harmonic oscillator and special type of motion called simple harmonic by using . what the dependence of motion. Examples include gravitational force the motion is on those exerted by the Earth on a simple pendulum properties. [SP 6.4, 7.2] and mass-spring oscillator. 3.B.3.2: The student a. For a spring that exerts a linear restoring is able to design a force, the period of a mass-spring oscillator plan and collect data increases with mass and decreases with in order to ascertain spring stiffness. the characteristics of b. For a simple pendulum, the period the motion of a system increases with the length of the pendulum undergoing oscillatory and decreases with the magnitude of the motion caused by a gravitational field. restoring force. [SP 4.2] c. Minima, maxima, and zeros of position, 3.B.3.3: The student can velocity, and acceleration are features of analyze data to identify harmonic motion. Students should be able to qualitative or quantitative calculate force and acceleration for any given relationships between displacement for an object oscillating on a given values and variables spring. (i.e., force, displacement, acceleration, velocity, Relevant Equations: period of motion, frequency, spring constant, string length, mass) associated with objects in oscillatory motion to use that data to determine the value of an unknown. [SP 2.2, 5.1] 3.B.3.4: The student is able to construct a qualitative and/or a quantitative explanation of oscillatory behavior given evidence of a restoring force. [SP 2.2, 6.2]

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Return to Table of Contents Table to Return Essential Knowledge Essential students need to (What know) structure with internal A system 5.B.2: in and changes energy, internal can have can result structure internal a system’s 1: [Physics energy. in internal in changes and simple oscillators includes mass-spring 2: includes charged Physics pendulums. and examining fields object in electric in with changes energy in internal changes configuration.] A system with internal structure can structure with internal A system 5.B.3: exists energy Potential energy. potential have if the objects withinwithin that a system forces. with conservative interact system force a conservative done by a. The work The work is independent of the path taken. to the external forces description is used for is used when the energy Potential system. parts between interactions internal are forces of the system. can result structure in the internal Changes b. Examples energy. in potential in changes and objects include mass-spring oscillators field. in a gravitational falling in a circuit potential in electric c. The change per unit energy in potential is the change of in the context 1: only [Physics charge. circuits.] Equations: Relevant Content Area 6: Simple Harmonic Motion Motion Harmonic 6: Simple Area Content AP Physics 1: Algebra-Based AP Physics

Learning Objectives Learning be students must (What to do) able The student 5.B.2.1: the to calculate is able of a behavior expected the using object system ignoring by model (i.e., in internal changes a to analyze structure) when the Then, situation. the student model fails, theof use can justify of energy conservation to calculate principles in internal the change in due to changes energy because structure internal a the object is actually [SP 1.4, 2.1] system. The student 5.B.3.1: to describe and is able and/or qualitative make predictions quantitative examples about everyday with internal of systems [SP 2.2, energy. potential 6.4, 7.2] The student is 5.B.3.2: quantitative to make able of thecalculations internal of a energy potential a description from system of that system. or diagram [SP 1.4, 2.2] The student 5.B.3.3: to apply is able reasoning mathematical a description to create potential of the internal of a system energy a description or from of the objects diagram in that and interactions system. [SP 1.4, 2.2] Course and Exam Description and Exam Course The energy of a The energy 5.B: is conserved. system Enduring Understanding Enduring concepts that (Core retain) students should 45 Content Outline Content Area 6: Simple Harmonic Motion

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

5.B: The energy of a 5.B.4.1: The student 5.B.4: The internal energy of a system ramework system is conserved. is able to describe and includes the kinetic energy of the objects that F make predictions about make up the system and the potential energy (Continued) the internal energy of of the configuration of the objects that make systems. [SP 6.4, 7.2] up the system. Course Course 5.B.4.2: The student is a. Since energy is constant in a closed system, able to calculate changes changes in a system’s potential energy can in kinetic energy and result in changes to the system’s kinetic potential energy of a energy. system, using information b. The changes in potential and kinetic from representations of energies in a system may be further that system. [SP 1.4, 2.1, constrained by the construction of the system. 2.2]

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b. For uniform circular motion of radius r, v motion of radius circular uniform For b. r), and a given (for to omega is proportional a Given omega). a given to r (for proportional T, students r and a period of rotation radius T. v = (2πr)/ apply and derive Essential Knowledge need to students (What know) in a particular reference 3.A.1: An observer can describe the motion of an frame object using such quantities as position, speed, and displacement, distance, velocity, acceleration. analogous are motion, there rotational a. For quantities such as angular position, angular and angular acceleration. velocity, Equations: Relevant Content Area 7: Torque and Rotational Motion Motion and Rotational 7: Torque Area Content AP Physics 1: Algebra-Based AP Physics

Learning Objectives must be students (What to do) able 3.A.1.1: The student the to express is able motion of an object using mathematical, narrative, and graphical [SP 1.5, representations. 2.1, 2.2] The interactions of an object with other objects can be objects can other with object an of The interactions described by forces. in between changes in systems result can Interactions systems. those are interactions of occur as a result that Changes constrained by conservation laws.

dea 3: dea4: dea5: I I I Course and Exam Description and Exam Course Enduring Understanding that concepts (Core retain) students should Big Big share 3.A: All forces certain common when characteristics observers by considered in inertial reference frames. Content Area 7: Torque and Rotational Motion Torque Content Area 7: Big 47 Content Outline Content Area 7: Torque and Rotational Motion

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

3.F: A force exerted on an 3.F.1.1: The student 3.F.1: Only the force component perpendicular ramework object can cause a torque is able to use to the line connecting the axis of rotation and F on that object. representations of the the point of application of the force results in relationship between force a torque about that axis.

and torque. [SP 1.4] a. The lever arm is the perpendicular distance Course Course 3.F.1.2: The student from the axis of rotation or revolution to the is able to compare the line of application of the force. torques on an object b. The magnitude of the torque is the product caused by various forces. of the magnitude of the lever arm and the [SP 1.4] magnitude of the force. 3.F.1.3: The student c. The net torque on a balanced system is is able to estimate the zero. torque on an object caused by various forces Relevant Equation: in comparison to other τ = r F = rFsin θ situations. [SP 2.3] ⊥ 3.F.1.4: The student Boundary Statement: is able to design an Quantities such as angular acceleration, experiment and analyze velocity, and momentum are defined as vector data testing a question quantities, but in Physics 1 the determination about torques in a of “direction” is limited to clockwise and balanced rigid system. counterclockwise with respect to a given axis [SP 4.1, 4.2, 5.1] of rotation. 3.F.1.5: The student is able to calculate torques on a two-dimensional system in static equilibrium, by examining a representation or model (such as a diagram or physical construction). [SP 1.4, 2.2]

3.F.2.1: The student is 3.F.2: The presence of a net torque along any able to make predictions axis will cause a rigid system to change its about the change in the rotational motion or an object to change its angular velocity about rotational motion about that axis. an axis for an object a. Rotational motion can be described in terms when forces exerted on of angular displacement, angular velocity, and the object cause a torque angular acceleration about a fixed axis. about that axis. [SP 6.4] b. Rotational motion of a point can be related 3.F.2.2: The student to linear motion of the point using the is able to plan data distance of the point from the axis of rotation. collection and analysis strategies designed to test c. The angular acceleration of an object or the relationship between rigid system can be calculated from the net a torque exerted on an torque and the rotational inertia of the object object and the change in or rigid system. angular velocity of that object about an axis. [SP 4.1, 4.2, 5.1]

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Δt F = rFsin τ ⊥ = LI ΔL = Essential Knowledge Essential students need to (What know) Equations: Relevant τ = r A torque exerted on an object can A torque exerted 3.F.3: the angular momentum of an object. change quantity, a. Angular momentum is a vector a right-hand by determined with its direction rule. momentum of a The magnitude of angular b. point object about an axis can be calculated the perpendicular distance multiplying by to the line of motion the axis of rotation from the magnitude of linear momentum. by c. The magnitude of angular momentum object can also be found of an extended the inertia by the rotational multiplying by Students do not need to angular velocity. rotational an object’s the for know equation the at exam. inertia,will be provided as it sense of what a qualitative have should They for example inertia, rotational affect factors inertia than a rotational a hoop has more why puck of the same mass and radius. in angular momentum of an d. The change of the average the product by object is given torque and the time the torque is exerted. Equations: Relevant L = mvr

Content Area 7: Torque and Rotational Motion Motion and Rotational 7: Torque Area Content AP Physics 1: Algebra-Based AP Physics

The student 3.F.3.1: the to predict is able of rotational behavior by collision situations that the same processes linear used to analyze are using collision situations between an analogy impulse and change of linear momentum and angular impulse of angular and change momentum. [SP 6.4, 7.2] In an unfamiliar 3.F.3.2: or using context beyond representations the student is equations, the to justify selection able routine of a mathematical in the change for to solve angular momentum of an torques object caused by on the object. exerted Learning Objectives Learning be students must (What to do) able [SP 2.1] The student 3.F.3.3: to plan data is able and analysis collection designed to test strategies between the relationship on an torques exerted in object and the change angular momentum of that object. [SP 4.1, 4.2, 5.1, 5.3] Course and Exam Description and Exam Course A force exerted on exerted 3.F: A force an object can cause a torque on that object. (Continued) Enduring Understanding Enduring concepts that (Core retain) students should 49 Content Outline Content Area 7: Torque and Rotational Motion

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

4.D: A net torque exerted 4.D.1.1: The student 4.D.1: Torque, angular velocity, angular ramework on a system by other is able to describe a acceleration, and angular momentum are F objects or systems will representation and use vectors and can be characterized as positive change the angular it to analyze a situation or negative depending upon whether they give momentum of the system. in which several forces rise to or correspond to counterclockwise or Course Course exerted on a rotating clockwise rotation with respect to an axis. system of rigidly Relevant Equations: connected objects change the angular velocity and angular momentum of the system. [SP 1.2, 1.4] 4.D.1.2: The student is able to plan data LI= collection strategies designed to establish that ΔL = τΔt torque, angular velocity, angular acceleration, and angular momentum can be predicted accurately when the variables are treated as being clockwise or counterclockwise with respect to a well-defined Boundary Statement: axis of rotation, and refine Students do not need to know the right hand the research question rule. A full dynamic treatment of rolling without based on the examination slipping—for instance, using forces and torques of data. [SP 3.2, 4.1, 4.2, to find the linear and angular acceleration of a 5.1, 5.3] cylinder rolling down a ramp—is not included in Physics 1.

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Return to Table of Contents Table to Return The angular momentum of a system may may of a system The angular momentum Δt Δt τ τ = = LI LI ΔL = ΔL = Essential Knowledge Essential students need to (What know) 4.D.2: with other objects due to interactions change or systems. with of a system a. The angular momentum is the sum of the to an axis of rotation respect of to that axis, angular momenta, with respect the up the system. objects that make angular momentum of an object about The b. by multiplying found be axis can a fixed the the of the momentum by particle the the axis to from perpendicular distance line of motion of the object. the angular momentum of a c. Alternatively, of the the product from can be found system inertia and its angular rotational system’s the to know Students do not need velocity. inertia, as rotational an object’s for equation should the They at exam. it will be provided inertia sense that rotational a qualitative have the when the mass is farther from is larger axis of rotation. Equations: Relevant in angular momentum is The change 4.D.3: torque and of the average the product by given during which the torque is the time interval exerted. Equations: Relevant Content Area 7: Torque and Rotational Motion Motion and Rotational 7: Torque Area Content AP Physics 1: Algebra-Based AP Physics

The student is 4.D.3.1: to use appropriate able to routines mathematical initial or for values calculate final angular momentum, in angularor change momentum of a system, torque or time or average during which the torque a in analyzing is exerted torque involving situation and angular momentum. [SP 2.2] The student is able 4.D.3.2: collectionto plan a data designe d to test strategy between the relationship the in angular change and momentum of a system of the average the product theapplied to torque system during and the time interval which the torque is exerted. [SP 4.1, 4.2] Learning Objectives Learning be students must (What to do) able The student is 4.D.2.1: to describe a model able system of a rotational and use that model to in a situation analyze which angular momentum due to interaction changes with other objects or [SP 1.2, 1.4] systems. The student 4.D.2.2: to plan a data is able and analysis collection to determine strategy in angular the change momentum of a system it to interactions and relate with other objects and [SP 4.2] systems. Course and Exam Description and Exam Course A net torque exerted 4.D: A net torque exerted other by on a system will objects or systems the angular change momentum of the system. (Continued) Enduring Understanding Enduring concepts that (Core retain) students should 51 Content Outline Content Area 7: Torque and Rotational Motion

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

5.E: The angular 5.E.1.1: The student is 5.E.1: If the net external torque exerted on the ramework momentum of a system is able to make qualitative system is zero, the angular momentum of the F conserved. predictions about the system does not change. angular momentum of Relevant Equations: a system for a situation Course Course in which there is no net LI= external torque. [SP 6.4, ΔL = τΔt 7.2] 5.E.1.2: The student is able to make calculations of quantities related to the angular momentum of a system when the net external torque on the system is zero. [SP 2.1, 2.2]

5.E.2.1: The student 5.E.2: The angular momentum of a system is able to describe or is determined by the locations and velocities calculate the angular of the objects that make up the system. The momentum and rotational rotational inertia of an object or system inertia of a system in depends upon the distribution of mass within terms of the locations the object or system. Changes in the radius of and velocities of objects a system or in the distribution of mass within that make up the system. the system result in changes in the system’s Students are expected to rotational inertia, and hence in its angular do qualitative reasoning velocity and linear speed for a given angular with compound objects. momentum. Examples include elliptical orbits Students are expected in an Earth-satellite system. Mathematical to do calculations with expressions for the moments of inertia will be a fixed set of extended provided where needed. Students will not be objects and point masses. expected to know the parallel axis theorem. [SP 2.2] Students do not need to know the equation for an object’s rotational inertia, as it will be provided at the exam. They should have a qualitative sense that rotational inertia is larger when the mass is farther from the axis of rotation. Relevant Equation: I = mr 2

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Return to Table of Contents Table to Return Δq Δt Boundary Statement: in occurs of electrostatics coverage Full the concepts to Physics 2. A basic introduction and positive and negative charges, are that there between and repulsion attraction the electrostatic is included in Physics 1 as well. these charges, only; Physics fields Physics 1 treats gravitational 2 treats and magnetic fields. electric There are only two kinds of electric kinds of electric two only are There 1.B.2: contain objects or systems Neutral charge. and negative equal quantities of positive with some of the exception charge, no electric that have fundamental particles charge. repel, objects and systems a. Like-charged objects and systems and unlike-charged attract. Equation: Relevant Essential Knowledge need to students (What know) The net is conserved. charge Electric 1.B.1: is equal to the sum of the of a system charge of all the objects in the system. charges of is a movement current a. An electrical a conductor. through charge of electrical loop is a closed A circuit b. current. Equation: Relevant I = AP Physics 1: Algebra-Based AP Physics Content Area 8: Electric Charge and Electric Force Force and Electric Charge 8: Electric Area Content

The student 1.B.2.1: to construct an is able of theexplanation two- model of electric charge based on evidence charge through produced [SP scientific practices. 6.2] Learning Objectives must students (What to do) be able The student is 1.B.1.1: claims about to make able phenomena based natural of electric on conservation [SP 6.4] charge. The student is 1.B.1.2: predictions, to make able of using the conservation the about charge, electric quantity sign and relative of objects of net charge various after or systems processes, charging of including conservation circuits. in simple charge [SP 6.4, 7.2] Objects and systems have properties systems have Objects as mass and and such structure. Systems internal may have charge. be objects can other with object an of The interactions described by forces. are interactions of occur as a result that Changes constrained by conservation laws.

Course and Exam Description and Exam Course Enduring Understanding that concepts (Core retain) students should Big Idea 3: Big Idea 5: Big is charge Electric 1.B: of an object a property that affects or system with its interactions other objects or systems containing charge. Content Area 8: Electric Charge and Electric Force Idea 1: Big 53 Content Outline Content Area 8: Electric Charge and Electric Force

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must (What students need to students should retain) be able to do) know)

1.B: Electric charge is 1.B.3.1: The student is 1.B.3: The smallest observed unit of charge ramework a property of an object able to challenge the that can be isolated is the electron charge, F or system that affects claim that an electric also known as the elementary charge. its interactions with charge smaller than the a. The magnitude of the elementary charge is other objects or systems elementary charge has equal to 1.6 x 10-19 coulombs. Course Course containing charge. been isolated. [SP 1.5, (Continued) 6.1, 7.2] b. Electrons have a negative elementary charge; protons have a positive elementary charge of equal magnitude, although the mass of a proton is much larger than the mass of an electron.

3.C: At the macroscopic 3.C.2.1: The student is 3.C.2: Electric force results from the level, forces can be able to use Coulomb’s interaction of one object that has an electric categorized as either law qualitatively and charge with another object that has an electric long-range (action-at-a- quantitatively to make charge. distance) forces or contact predictions about the a. Electric forces dominate the properties forces. interaction between two of the objects in our everyday experiences. electric point charges However, the large number of particle (interactions between interactions that occur make it more collections of electric convenient to treat everyday forces in terms of point charges are not nonfundamental forces called contact forces, covered in Physics 1 and such as normal force, friction, and tension. instead are restricted to Physics 2). b. Electric forces may be attractive or [SP 2.2, 6.4] repulsive, depending upon the charges on the objects involved. 3.C.2.2: The student is able to connect the Relevant Equations: concepts of gravitational force and electric force to compare similarities and differences between the forces. [See SP 7.2]

5.A: Certain quantities 5.A.2.1: The student 5.A.2: For all systems under all are conserved, in the is able to define open circumstances, energy, charge, linear sense that the changes and closed systems momentum, and angular momentum are of those quantities in a for everyday situations conserved. For an isolated or a closed system, given system are always and apply conservation conserved quantities are constant. An open equal to the transfer of concepts for energy, system is one that exchanges any conserved that quantity to or from charge and linear quantity with its surroundings. the system by all possible momentum to those interactions with other situations. [SP 6.4, 7.2] systems.

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Return to Table of Contents Table to Return Δq Δq Boundary Statement: affect to temperature Knowledge of what causes resistivity is not part of Physics 1. Essential Knowledge need to students (What know) The net is conserved. charge Electric 1.B.1: is equal to the sum of the of a system charge of all the objects in the system. charges of is a movement current a. An electrical a conductor. through charge of electrical loop is a closed A circuit b. current. Equation: Relevant I = resistivity. called has a property 1.E.2: Matter depends on its of a material a. The resistivity structure. and atomic molecular depends on the temperature The resistivity b. with changes Resistivity of the material. temperature. Equation: Relevant Content Area 9: DC Circuits 9: DC Area Content AP Physics 1: Algebra-Based AP Physics

1.E.2.1: The student to choose and is able the of selection justify needed to determine data a given for resistivity [SP 4.1] material. Learning Objectives must students (What to do) be able The student is 1.B.1.1: claims about to make able phenomena based natural of electric on conservation [SP 6.4] charge. The student is 1.B.1.2: predictions, to make able of using the conservation the about charge, electric quantity sign and relative of objects of net charge various after or systems processes, charging of including conservation circuits. in simple charge [SP 6.4, 7.2] Objects and systems have properties systems have Objects as mass and and such structure. Systems internal may have charge. are interactions of occur as a result that Changes constrained by conservation laws.

Course and Exam Description and Exam Course Materials have have 1.E: Materials macroscopic many that result properties and the arrangement from the of atoms interactions that make and molecules up the material. Big Idea 5: Big Enduring Understanding that concepts (Core retain) students should is charge Electric 1.B: of an object a property that affects or system with its interactions other objects or systems containing charge. Content Area 9: Circuits DC Idea 1: Big 55 Content Outline Content Area 9: DC Circuits

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must (What students need to students should retain) be able to do) know)

5.B: The energy of a 5.B.9.1: The student 5.B.9: Kirchhoff’s loop rule describes ramework system is conserved. is able to construct or conservation of energy in electrical circuits. F interpret a graph of the [The application of Kirchhoff’s laws to energy changes within circuits is introduced in Physics 1 and further an electrical circuit with developed in Physics 2 in the context of Course Course only a single battery and more complex circuits, including those with resistors in series and/or capacitors.] in, at most, one parallel The potential difference across an ideal branch as an application battery is also referred to as the emf of the of the conservation of battery, represented as ε. [Non-ideal batteries energy (Kirchhoff’s loop are not covered in Physics 1.] rule). [SP 1.1, 1.4] a. Energy changes in simple electrical circuits 5.B.9.2: The student is are conveniently represented in terms of able to apply conservation energy change per charge moving through a of energy concepts to the battery and a resistor. design of an experiment that will demonstrate the b. Since electric potential difference times validity of Kirchhoff’s loop charge is energy, and energy is conserved, rule (∑ΔV=0) in a circuit the sum of the potential differences about any with only a battery and closed loop must add to zero. resistors either in series c. The electric potential difference across a or in, at most, one pair of resistor is given by the product of the current parallel branches. [SP 4.2, and the resistance. 6.4, 7.2] d. The rate at which energy is transferred from 5.B.9.3: The student is a resistor is equal to the product of the electric able to apply conservation potential difference across the resistor and the of energy (Kirchhoff’s current through the resistor. loop rule) in calculations involving the total electric Relevant Equations: potential difference for ΔV I = complete circuit loops R with only a single battery P = I Δ V and resistors in series and/or in, at most, one parallel branch. [SP 2.2, 6.4, 7.2]

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Return to Table of Contents Table to Return R ΔV Δq Δt P = I Δ V Essential Knowledge Essential students need to (What know) I = Kirchhoff’s junction rule describes junction rule the Kirchhoff’s 5.C.3: in electrical charge of electric conservation current is conserved, charge Since circuits. in each junction at must be conserved that include circuits Examples the circuit. in series and parallel. combine resistors in with resistors circuits 1: covers [Physics one branch, with most one parallel at series, 2: includes capacitors Physics only. battery with circuits For situations. in steady-state to limited be should situations capacitors, and a is closed, circuit after just open circuit, is closed.] the circuit time after long Equations: Relevant I = Content Area 9: DC Circuits 9: DC Area Content AP Physics 1: Algebra-Based AP Physics

Learning Objectives Learning students must (What do) to be able The student is 5.C.3.1: conservation to apply able charge of electric junction rule) (Kirchhoff’s to the of comparison in various current electric segments of an electrical with a single circuit in and resistors battery most, series and in, at branch one parallel those how and predict change would values of the if configurations [SP changed. are circuit 6.4, 7.2] The student 5.C.3.2: to design an is able of an investigation with one circuit electrical in which resistors or more of conservation evidence be can charge of electric and analyzed. collected [SP 4.1, 4.2, 5.1] The student is 5.C.3.3: to use a description able diagram or schematic to circuit of an electrical values unknown calculate in various of current of segments or branches [SP 1.4, 2.2] the circuit. Course and Exam Description and Exam Course The electric charge of charge The electric 5.C: conserved. is a system Enduring Understanding Enduring concepts that (Core retain) students should 57 Content Outline Content Area 10: Mechanical Waves and Sound

Content Area 10: Mechanical Waves and Sound Big Idea 6: Waves can transfer energy and momentum from one location to another without the permanent transfer of mass ramework

F and serve as a mathematical model for the description of other phenomena. Course Course Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

6.A: A wave is a traveling 6.A.1.1: The student 6.A.1: Waves can propagate via different disturbance that transfers is able to use a visual oscillation modes such as transverse and energy and momentum. representation to longitudinal. construct an explanation a. Mechanical waves can be either transverse of the distinction or longitudinal. Examples include waves on a between transverse and stretched string and sound waves. longitudinal waves by focusing on the vibration b. This includes, as part of the mechanism that generates the wave. of “propagation,” the idea that the speed of [SP 6.2] a wave depends only on properties of the medium. 6.A.1.2: The student is able to describe c. The propagation of sound waves included representations in this EK includes the idea that the traveling of transverse and disturbance consists of pressure variations longitudinal waves. [SP coupled to displacement variations. 1.2] d. This applies to both periodic waves and to wave pulses.

Boundary Statement: Physics 1 treats mechanical waves only. Mathematical modeling of waves using sines or cosines is included in Physics 2. Superposition of no more than two wave pulses and properties of standing waves is evaluated in Physics 1. Interference is revisited in Physics 2, where two-source interference and diffraction may be demonstrated with mechanical waves, leading to the development of these concepts in the context of electromagnetic waves, the focus of Physics 2.

6.A.2.1: The student is 6.A.2: For propagation, mechanical waves able to describe sound require a medium, while electromagnetic in terms of transfer of waves do not require a physical medium. energy and momentum Examples include light traveling through a in a medium and relate vacuum and sound not traveling through a the concepts to everyday vacuum. examples. [SP 6.4, 7.2]. Boundary Statement: Electromagnetic waves are not tested in Physics 1. This applies to both periodic waves and wave pulses.

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Return to Table of Contents Table to Return Essential Knowledge Essential students need to (What know) 6.A.3: The amplitude is the maximum its equilibrium from displacement of a wave value. a. The amplitude is the maximum equilibrium of thewave. displacement from either by be represented may A sound wave or the or displacement of atoms the pressure both periodic waves This covers molecules. pulses. and wave of a sound wave amplitude pressure The b. local between is the difference maximum pressure. and atmospheric pressure carried by the energy 6.A.4: Classically, with and increases depends upon a wave waves. include sound amplitude. Examples to both greater a. Higher amplitude refers displacement and greater variations pressure variations. and include both periodic waves Examples b. pulses. wave the period is the a periodic wave, For 6.B.1: is the The frequency time of the wave. repeat per unit of the wave of repetitions number time. pressure a. In a periodic sound wave, are and displacement variations variations and with theboth same frequency. present Equation: Relevant For a periodic wave, the wavelength is the wavelength a periodic wave, For 6.B.2: distance of the wave. the repeat The student is The student Content Area 10: Mechanical Waves and Sound and Sound Waves 10: Mechanical Area Content AP Physics 1: Algebra-Based AP Physics

6.B.2.1: Learning Objectives Learning students must be(What to do) able 6.A.3.1: The student is to use graphical able of a representation periodic mechanical the to determine wave amplitude of the wave. [SP 1.4] 6.A.4.1: The student is to explain and/or able how qualitatively predict a carried by the energy to the relates sound wave amplitude of the wave, thisand/or concept apply example. to a real-world [SP 6.4] 6.B.1.1: to use a graphical able of a periodic representation (position mechanical wave time) to determine versus of the period and frequency describe how and the wave in the frequency a change of modify features would [SP the representation. 1.4, 2.2] is able to use a visual is able of a representation periodic mechanical wave wavelength to determine [SP 1.4] of the wave. Course and Exam Description and Exam Course A wave is a traveling is a traveling 6.A: A wave disturbance that transfers and momentum. energy (Continued) A periodic wave 6.B: as is one that repeats a function of both time and position and can its be described by amplitude, frequency, speed, and wavelength, energy. Enduring Understanding Enduring concepts that (Core retain) students should 59 Content Outline Content Area 10: Mechanical Waves and Sound

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

6.B: A periodic wave 6.B.4.1: The student 6.B.4: For a periodic wave, wavelength is the ramework is one that repeats is able to design an ratio of speed over frequency. F as a function of both experiment to determine Relevant Equation: time and position the relationship between and can be described periodic wave speed, Course Course by its amplitude, wavelength, and frequency, wavelength, frequency and relate these speed, and energy. concepts to everyday (Continued) examples. [SP 4.2, 5.1, 7.2]

6.B.5.1: The student is 6.B.5: The observed frequency of a wave able to create or use a depends on the relative motion of source and wave front diagram to observer. This is a qualitative treatment only. demonstrate or interpret qualitatively the observed frequency of a wave, dependent upon relative motions of source and observer. [SP 1.4]

6.D: Interference and 6.D.1.1: The student 6.D.1: Two or more wave pulses can interact superposition lead to is able to use in such a way as to produce amplitude standing waves and beats. representations of variations in the resultant wave. When two individual pulses and pulses cross, they travel through each other; construct representations they do not bounce off each other. Where the to model the interaction pulses overlap, the resulting displacement can of two wave pulses to be determined by adding the displacements of analyze the superposition the two pulses. This is called superposition. of two pulses. [SP 1.1, 1.4] 6.D.1.2: The student is able to design a suitable experiment and analyze data illustrating the superposition of mechanical waves (only for wave pulses or standing waves). [SP 4.2, 5.1] 6.D.1.3: The student is able to design a plan for collecting data to quantify the amplitude variations when two or more traveling waves or wave pulses interact in a given medium. [SP 4.2]

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Return to Table of Contents Table to Return Essential Knowledge Essential students need to (What know) can waves traveling more or Two 6.D.2: amplitude as to produce in such a way interact wave. in the resultant variations Standing waves are the result of the the result are Standing waves 6.D.3: that waves addition of incident and reflected nodes and region and have confined to a are on a fixed include waves Examples antinodes. in both length and sound waves of string and open tubes. closed even pulses, wave and waves of a. Reflection in is covered is not created, if a standing wave 1. Physics nodes pressure waves, standing sound For b. and to displacement antinodes, correspond the open end of a example, For vice versa. node because the pressure tube is a pressure air pressure equalizes with the surrounding The closed does not oscillate. and therefore end of a tube is a displacement node because to thethe end is blocked closed air adjacent oscillating. from Content Area 10: Mechanical Waves and Sound and Sound Waves 10: Mechanical Area Content AP Physics 1: Algebra-Based AP Physics

Learning Objectives Learning students must be(What to do) able The student is 6.D.2.1: or data to analyze able or evaluate observations of theevidence interaction traveling or more of two in one or two waves circular dimensions (i.e., to evaluate fronts) wave in resultant the variations [SP 5.1] amplitudes. The student is 6.D.3.1: a scientific to refine able to question related and standing waves plan for design a detailed thethatexperiment be can the to examine conducted phenomenon qualitatively [SP 2.1, or quantitatively. 3.2, 4.2] The student is 6.D.3.2: properties to predict able that of standing waves the addition from result of incident and reflected confined to that are waves nodes and have a region [SP 6.4] and antinodes. The student is 6.D.3.3: collection to plan data able the predict strategies, outcome based on the under test, relationship analysis, data perform evidence evaluate to the prediction, compared discrepancy explain any revise and, if necessary, among the relationship for responsible variables establishing standing on a string or in a waves [SP 3.2, 4.1, column of air. 5.1, 5.2, 5.3] The student is able 6.D.3.4: to describe representations and models of situations in which standing waves the addition from result of incident and reflected region. confined to a waves [SP 1.2] Course and Exam Description and Exam Course Interference and and 6.D: Interference to superposition lead and beats. standing waves (Continued) Enduring Understanding Enduring concepts that (Core retain) students should 61 Content Outline Content Area 10: Mechanical Waves and Sound

Enduring Understanding Learning Objectives Essential Knowledge (Core concepts that (What students must be (What students need to students should retain) able to do) know)

6.D: Interference and 6.D.4.1: The student is 6.D.4: The possible wavelengths of a standing ramework superposition lead to able to challenge with wave are determined by the size of the region F standing waves and beats. evidence the claim to which it is confined. that the wavelengths (Continued) a. A standing wave with zero amplitude at of standing waves both ends can only have certain wavelengths. Course Course are determined by the Examples include fundamental frequencies frequency of the source and harmonics. regardless of the size of the region. [SP 1.5, 6.1] b. Other boundary conditions or other region sizes will result in different sets of possible 6.D.4.2: The student wavelengths. is able to calculate wavelengths and c. The term first harmonic refers to the frequencies (if given standing waves corresponding to the wave speed) of standing fundamental frequency, i.e., the lowest waves based on boundary frequency corresponding to a standing wave. conditions and length The second harmonic is the standing wave of region within which corresponding to the second lowest frequency the wave is confined, that generates a standing wave in the given and calculate numerical scenario. values of wavelengths and d. Resonance is another term for standing frequencies. Examples sound wave. include musical instruments. [SP 2.2] Relevant Equations:

6.D.5.1: The student 6.D.5: Beats arise from the addition of waves is able to use a visual of slightly different frequency. representation to explain a. Because of the different frequencies, the how waves of slightly two waves are sometimes in phase and different frequency give sometimes out of phase. The resulting rise to the phenomenon regularly spaced amplitude changes are called of beats. beats. Examples include the tuning of an [SP 1.2] instrument. b. The beat frequency is the difference in frequency between the two waves. c. In Physics 1, only qualitative understanding of EK 6.D.5 is necessary.

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Return to Table of Contents Table to Return References References . 2nd ed. Alexandria, VA: VA: . 2nd ed. Alexandria, http://padi.sri.com/downloads/ An Introduction to PADI Task Templates Templates Task PADI to An Introduction Evidence-Centered Assessment Design: Layers, Design: Layers, Assessment Evidence-Centered Understanding by Design by Understanding AP Physics 1: Algebra-Based AP Physics http://padi.sri.com/downloads/TR3_Templates.pdf (PADI Technical Report 9). Menlo Park, CA: SRI International SRI International CA: Park, 9). Menlo Report Technical (PADI

Course and Exam Description and Exam Course TR9_ECD.pdf and L. Hamel. 2005. Mislevy, M. M., R. J. Riconscente, Supervision and Curriculum Development. for Association and University of Maryland. Retrieved May 1, 2006, from 1, 2006, from May Retrieved of Maryland. and University Structures, and Terminology and Terminology Structures, of Maryland. and University SRI International CA: Park, 3). Menlo Report Technical (PADI 1, 2006, from May Retrieved 2005. McTighe. G., and J. Wiggins, References renowned of nationally on groups relies process development exam and The AP course in secondary and experts professionals each discipline, including in subject-matter These experts ensure organizations. professional as from as well postsecondary education that the courses available, information the most up-to-date reflect and exams that AP courses is assessed and that student proficiency course, a college-level for appropriate are and exams and and abilities identified in skills, the course that the knowledge, help ensure To properly. both curriculum for foundation strong as a in a manner that will serve articulated are exam and AP 1: Algebra-Based AP Physics experts for theand assessment design, subject-matter works. the following and tools from utilized principles 2: Algebra-Based Physics 2005. Riconscente. and M. M. R. J., Mislevy, 63 64 Lab Investigations Inquiry InstructionintheAPScienceClassroomInquiry and instruction with these practices these and instructionwith inmind. integrated course the content, with willbeable andthey todesignlaboratory investigations course. APPhysics teachers learning objectives the willseewithin practices how these are and university faculty end ofanintroductory expect studentstopossessat the college-level work scientistsengage that aspectsofthe important level in,at the ofcompetence college that The sciencepractices content course aligntothe that outlineofthe framework capture data, apply mathematical routines, develop explanations, andcommunicate work. abouttheir science practices designplansfor asthey experiments, make predictions, collect andanalyze Curricular Requirements by providing for opportunities studentstoengage seven inthe Inquiry-based laboratory APPhysics the experiencessupport 1course andAPCourse Audit Investigations Laboratory The AP Physics 1:Algebra-Based The 2014 Classroom Science in AP the Instruction Inquiry described in investigate physical meaningfulquestionsaboutthe bestpractices world the andalignwith AAPT 1992).Aninquiryapproach tolaboratory work engages andinspires studentsto teamwork, criticalthinking, andcommitmenttolife-long learning (NSF1996,NSF, 2012, curriculafor intheir include opportunities studentstodevelop skillsincommunication, recommendations by National ScienceFoundation the scienceteachers (NSF)that should investigations infour incremental ways: approach ofRezba, (1971)andthat Auldridge, andRhea(1999)defineinquiryinstruction for andproblem-solvingof critical-thinking skillsandabilities. Adaptations ofHerron’s increasingwith studentinvolvement development tohelp enhanceinquirylearning andthe the APclassroomScientific inquiryexperiencesin should bedesignedandimplemented learning insciencelaboratories from National Research the Council.

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Lab Investigations 65

are Return to Table of Contents Table © 2017 The College Board Return to Table of Contents Table to Return ; teachers are encouraged to develop develop to encouraged are ; teachers AP Physics 1: Algebra-Based AP Physics not as required activities not as required

Expectations for Analysis of Uncertainty in Laboratory Investigations Uncertainty of Analysis Expectations for Investigations in Laboratory

AP Physics 1 and 2 Inquiry-Based Manual Lab Investigations: A Teacher’s Course and Exam Description and Exam Course Teachers are expected to devote a minimum of 25 percent of instructional time to laboratory of instructional time to laboratory a minimum of 25 percent to devote expected are Teachers with an opportunity to engage be provided students should Additionally, in thiswork course. emphasizes 1 course The AP Physics investigations. inquiry-based in a minimum of seven students limiting the scope of content, By of content. breadth over depth of understanding conceptual experiences that will develop learning in inquiry-based time to engage more have this Applying expertise in the building science practices. while of content understanding than time simple more takes typically investigations to laboratory instructional approach to teachers will allow breadth of content reduced the however labs; verification/confirmation time that must be of course of 25 percent curricular requirements Audit meet the AP Course work. laboratory devoted The labs in the Time andResources as models, to serve intended the learning labs that address inquiry-based or student-directed their teacher-guided own also consider supporting their should physical They framework. in the course objectives by developed such as PhET simulations online simulations, with work interactive, laboratory Boulder. of Colorado, the University Some colleges and universities expect students to submit a laboratory notebook to receive to receive notebook expect students to submit a laboratory and universities Some colleges students the emphasis on time spent in the laboratory, Given courses. laboratory for credit mean, by including and supported analysis to the methods of error be introduced should or the and linear regression, of error, propagation error, percentage deviation, standard withfamiliar be to students expect will methods these Colleges fit. best of line a of calculation experiments they some of the least laboratory on at the carried out procedures and to have reduced significantly have calculators and since the particularly use of computers undertake, on their computations own. to perform students the need for ExpectationsAnalysis for Uncertainty of in Laboratory Investigations Typically, the level of investigations in an AP classroom should focus primarily on the the on primarily focus should in an AP classroom of investigations the level Typically, on student depending However, open inquiry. guided inquiry and between continuum involving a sequence might incorporate experience laboratory withfamiliarity a given a topic, carry out a simple might first instance, students or a subset of them. For levels all four familiarizes also to them withthat equipment and then proceed investigation confirmation with practice more the into and gives topic deeply more inquiry that probes a structured to design/ with a question and asked be presented that point students would equipment. At then that to questions could lead of results A class discussion their procedure. select own in open inquiry. groups by different differently be explored could in the However, to students. natural questions and inquiry is actually The idea of asking teacher- more developed have to them as they may seem natural not setting it may classroom As students experience courses. lab previous in habits and expectations procedural directed they guidance, with teacher less investigations self-directed more opportunities for more teacher The to inquiry. and approach in their reasoning sophisticated will become more — during class and in the the course throughout inquiry habits in students can promote of the of planning of experiments and manipulation more handing over — by laboratory to students. equipment over 65 66 Lab Investigations References National Research Council. References AP Physics 1:Algebra-Based Press, 2006. Report: Investigations inHighSchoolScience.Washington, DC:TheNational Academies Singer, SusanR.,Margaret L.Hilton,andHeidiA.Schweingruber. America’s Lab RoleOfLabs.cfm Position Paper, 1992.Accessed onJuly 27,2013. The Role ofLabsinHighSchoolPhysics andCoreConcepts, Ideas National Research Council. National Academies Press, 1996.

. Washington, DC:TheNational Academies Press, 2012. National Science Education Standards A Framework for K–12 Science Education: Practices, Crosscutting

Course andExam Description , AmericanAssociation ofPhysics Teachers (AAPT), http://www.aapt.org/resources/policy/ . Washington, DC:The Return to Table ofContents © 2017TheCollege Board Table ofContents

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The AP Physics 1 Exam 67

5 Return to 45 1 1 3 Total – 50 Total Total – 5 Total Number of Questions Table of Contents Table © 2017 The College Board Exam Information Information Exam Return to Table of Contents Table to Return Question Type Multiple Correct – Items with – Items Correct B: Multiple Part answers correct two Multiple Choice – Discrete Choice – Discrete A: Multiple Part in Sets and Items Items Experimental Design Translation Qualitative/Quantitative Short-Answer 50% of exam 50% of exam score 50% of exam 50% of exam score Scoring AP Physics 1: Algebra-Based AP Physics

Timing One hour and 30 minutes One hour and 30 minutes Experimental design — Pertains to designing and describing an investigation, analysis of of analysis to designing and describing an investigation, Experimental design — Pertains or explain phenomena patterns to identify authentic and observations lab data, and quantitative between translating — Requires translation Qualitative/quantitative reasoning and justification qualitative argument coherent a paragraph-length questions — One of which will require Short-answer Solve problems mathematically — including symbolically — but with less emphasis on only — but with on only emphasis less symbolically — including mathematically problems Solve solutions used for routines mathematical conceptual models and develop Interpret experiences to design during laboratory skills developed and analytical knowledge Transfer conclusions based on evidence. draw and data and describe experiments and analyze Provide both qualitative and quantitative explanations, reasoning, or justification of of or justification reasoning, explanations, and quantitative both qualitative Provide and theories principles in physics grounded phenomena, physical n n n n n n n n n n n n n n Multiple Choice Multiple Course and Exam Description and Exam Course Section I: II: Free Response II: Free Section I in the AP Physics 1 exam consists of 50 multiple-choice questions, either as discrete either questions, discrete as consists of 50 multiple-choice 1 exam Section I in the AP Physics and the knowledge questions that represent or multi-correct sets, questions in questions, framework, in the course objectives 1 learning outlined in the AP Physics science practices will be in questions Multi-correct to apply. and be able understand which students should to indicate and will B) section of the portion of the (Part multiple-choice exam a separate each question in the stimulus. options for the correct students to select two a total questions that each student will have types of free-response Section II contains three types are: question The three complete. to of one hour and 30 minutes Exam Exam Information The response. and free choice sections: multiple two consists of 1 exam The AP Physics section of section and a free-response and includes a multiple-choice long is 3 hours exam half of each student’s for section accounts each. The multiple-choice one hour and 30 minutes the other for half. Both section accounts sections include the and free-response grade, exam to in order science practices their and associated thequestions aligned to objectives learning ability to: assess students’ The AP Physics 1: Algebra-BasedTheAP Physics 1: 67 Exam Information Student Work for Free-Response Sections

The sample exam questions in this course and exam description represent the kinds of questions that are included on the AP Physics 1 exam. The concepts, content, application of science practices, and level of difficulty in these sample questions are comparable to what students will encounter on an actual AP Exam. Each sample multiple-choice and free- response question is followed by a text box that shows each question’s alignment with the learning objectives and science practices provided in the AP Physics 1 course framework. Multiple-choice questions will contain four answer options. A student’s total score on the multiple-choice section is based on the number of questions answered correctly. Points are not deducted for incorrect answers or unanswered questions.

Student Work for Free-Response Sections In scoring the free-response sections, credit for the answers depends on the quality of the solutions and the explanations given; partial solutions may receive partial credit, so students are advised to show all their work. Correct answers without supporting work may lose credit. This is especially true when students are asked specifically to justify their answers, in which case the AP Exam Readers are looking for some verbal or mathematical analysis that shows how the students arrived at their answers. Also, all final numerical answers should include appropriate units.

Terms Defined On the AP Physics 1 exam the words “describe,” “explain,” “justify,” “calculate,” “derive,” “what is,” “determine,” “sketch,” “plot,” “draw,” “label,” “design,” and “outline” have precise meanings.

The AP Physics 1 Exam The AP Physics Students should pay careful attention to these words in order to obtain maximum credit and should avoid including irrelevant or extraneous material in their answers.

nn Students will be asked both to “describe” and “explain” natural phenomena. Both terms require the ability to demonstrate an understanding of physics principles by providing an accurate and coherent description or explanation. Students will also be asked to “justify” a previously given answer. A justification is an argument supported by evidence. Evidence may consist of statements of physical principles, equations, calculations, data, graphs, and diagrams as appropriate. The argument, or equations used to support justifications and explanations, may in some cases refer to fundamental ideas or relations in physics, such as Newton’s laws, conservation of energy, or Bernoulli’s equation. In other cases, the justification or explanation may take the form of analyzing the behavior of an equation for large or small values of a variable in the equation. nn “Calculate” means that a student is expected to show work leading to a final answer, which may be algebraic but more often is numerical. “Derive” is more specific and indicates that the students need to begin their solutions with one or more fundamental equations, such as those given on the AP Physics 1 Exam equation sheet. The final answer, usually algebraic, is then obtained through the appropriate use of mathematics. “What is” and “determine” are indicators that work need not necessarily be explicitly shown to obtain full credit. Showing work leading to answers is a good idea, as it may earn a student partial credit in the case of an incorrect answer. Strict rules regarding significant digits are usually not applied to the scoring of numerical answers. However, in some cases, answers containing too many digits may be penalized. In general, two to four significant digits are acceptable. Exceptions to these guidelines usually occur when rounding makes a difference in obtaining a reasonable answer.

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outline Return to Table of Contents Table to Return ” an experiment or “ design The Paragraph-Length Response Response The Paragraph-Length the forces (not components) that act on the [object],” where (not components) that act on the where [object],” the forces ” relate to student-produced graphs. “Sketch” means to draw means to draw “Sketch” graphs. to student-produced ” relate plot AP Physics 1: Algebra-Based AP Physics

label ” and “ and draw sketch [object] is replaced by a reference specific to the question, such as “the car when it reaches reaches specific to the question, such as “the car when it a reference by [object] is replaced in the will be scored in the included diagram the components that are top of the hill.” Any subsequent part asking for in any In addition, forces. or extraneous as incorrect same way will be included: the following use of the diagram, make typically a solution that would in part assist in your [x] to shown other have anything than you what need to draw “If you in part [x].” This will give to the add anything figure NOT Do solution, use the space below. components that are any showing students the diagram opportunity to construct a working be scored. will not This second diagram to the solution of the problem. appropriate Some questions will require students to “ Some questions will require Exam questions that require the drawing of free-body or force diagrams will direct the will direct diagrams force or of free-body the drawing questions that require Exam students to “ Students are a guiding question. answer would a specific phenomenon or that investigates in that specifies the necessary steps of statements sequence an orderly to provide expected the phenomenon. the question or investigate answer needed to reasonably the investigation The words “ The words a graph that illustrates key trends in a particular relationship, such as slope, curvature, curvature, such as slope, in a particular relationship, trends key that illustrates a graph in required not points are data scaling or specific Numerical or asymptote(s). intercept(s), on the grid provided, in the problem the points given data means to draw “Plot” a sketch. provided. the when none are and units or indicating scale scale either using the given n n n n n n Course and Exam Description and Exam Course The Paragraph-Length Response that uses argument consist of a coherent to a question should response A paragraph-length to expository fashion in a logical, in the question and proceeds presented the information a conclusion. at arrive demonstrate so that they may response a paragraph-length to give asked are students AP Physics expository in a reasoned, situation of a physical their understanding their ability to communicate and sequential description of organized, a coherent, be should response A student’s analysis. principles, physical cite evidence, from argue should The response of a situation. the analysis not include should The presentation thinking to the reader. the student’s present and clearly reading. sense on the first make It should information. extraneous than present rather a paragraph, of theThe style exposition is to explain and/or describe, like and length, not long be of moderate and should derivation, algebraic or a purely a calculation elaborate. as does a principles, physics correct will earn points for response A paragraph-length not be earned if a may full credit question. However, other free-response to any response in a logical not presented principles of the following: contains any response paragraph-length with little or diagrams equations or primarily within an argument, digressions lengthy order, linking prose. graphs, include, as needed, diagrams, may the 1 exam argument On the AP Physics of such a The style to support the and perhaps calculations line of reasoning. equations, a mix of typically which are in textbooks, problems be seen in the example may response of a situation. analysis an orderly etc., that present diagrams, equations, statements, prose and construct a situation to both be able analyze the is that students should goal reiterate, To of physics and principles evidence exposition that cites sequenced, well-reasoned a coherent, reading. sense on the first and that makes 69 Exam Information Expectations for the Analysis of Uncertainty

Expectations for the Analysis of Uncertainty On the AP Physics 1 exam, students will not need to calculate uncertainty but will need to demonstrate understanding of the principles of uncertainty. In general, multiple-choice questions on the AP Physics 1 exam will deal primarily with qualitative assessment of uncertainty, while free-response laboratory questions may require some quantitative understanding of uncertainty as described below. Experiment and data analysis questions on the AP Physics 1 exam will not require students to calculate standard deviations or carry out the propagation of error or a linear regression. Students will be expected to estimate a line of best fit to data that they plot or to a plot they are given. Students may be expected to discuss which measurement or variable in a procedure contributes most to overall uncertainty in the final result and on conclusions drawn from a given data set. They should recognize that there may be no significant difference between two reported measurements if they differ by less than the smallest difference that can be discerned on the instrument used to make the measurements. They should be able to reason in terms of percentage error and to report results of calculations to an appropriate number of significant digits. Students are also expected to be able to articulate the effects of error and error propagation on conclusions drawn from a given data set and how results and conclusions would be affected by changing the number of measurements, measurement techniques, or the precision of measurements. Students should be able to review and critique an experimental design or procedure and decide whether the conclusions can be justified based on the procedure and the evidence presented.

Calculators and Equation Tables Students will be allowed to use a calculator on the entire AP Physics 1 exam — including both the multiple-choice and free-response sections. Scientific or graphing calculators may be The AP Physics 1 Exam The AP Physics used, provided that they don’t have any unapproved features or capabilities. A list of approved graphing calculators is available at https://apstudent.collegeboard.org/takingtheexam/exam- policies/calculator-policy. Calculator memories do not need to be cleared before or after the exam. Since graphing calculators can be used to store data, including text, proctors should monitor that students are using their calculators appropriately. Communication between calculators is prohibited during the exam administration. Attempts by students to use the calculator to remove exam questions and/or answers from the room may result in the invalidation of AP Exam scores. The policy regarding the use of calculators on the AP Physics 1 exam was developed to address the rapid expansion of the capabilities of calculators, which include not only programming and graphing functions but also the availability of stored equations and other data. Students should be allowed to use the calculators to which they are accustomed. However, students should be encouraged to develop their skills in estimating answers and orders of magnitude quickly and in recognizing answers that are physically unreasonable or unlikely. Tables containing equations commonly used in physics will be provided for students to use during the entire AP Physics 1 exam. In general, the equations for each year’s exam are printed and distributed with the course and exam description at least a year in advance so that students can become accustomed to using them throughout the year. However, because the equation tables will be provided with the exam, students will NOT be allowed to bring their own copies to the exam room. The latest version of the equations and formulas list is included in Appendix B to this course and exam description. One of the purposes of providing the tables of commonly employed equations for use with the exam is to address the issue of equity for those students who do not have access to equations stored in their calculators. The availability of these equations to all students means that in the scoring of the exam, little or no credit will be awarded for simply writing down equations or for answers unsupported by explanations or logical development.

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Return to Table of Contents Table to Return Time Management Management Time AP Physics 1: Algebra-Based AP Physics

Course and Exam Description and Exam Course Time Management Management Time all parts of the exam. them their to complete to manage time to allow Students need to learn to the next question; to move not forced are but students proctors, is announced by left Time not wind up with enough time to their budget time, they may thus if they do not properly questions in the all in Section I and all the questions multiple-choice free-response complete to under timed conditions prior exam taking a practice from benefit often Section II. Students the actual administration. In general, the purpose of allowing calculators and equation sheets to be used in both used in both sheets to be and equation calculators the of allowing purpose In general, of and application emphasis on the understanding thesections of is to place greater exam a writing essays, and problems solving For and concepts. principles physical fundamental is no equations, of stored availability or the calculator, graphing scientific or sophisticated involved. of the physics grasp a thorough for substitute 71 Multiple-Choice Questions

Sample Questions for the AP Physics 1 Exam

Multiple-Choice Questions

NOTE: To simplify calculations, you may use g = 10 m/s2 in all problems.

Directions: Each of the questions or incomplete statements below is followed by four suggested answers or completions. Select the one that is best in each case and then fill in the corresponding circle on the answer sheet.

1. An object is moving in the positive x-direction while a net force directed along the x-axis is exerted on the object. The figure above shows the force as a function of position. What is the net work done on the object over the distance shown? Sample Questions (A) (B) (C) (D)

Enduring Understanding Learning Objective Science Practices

5.B: The energy of a 5.B.5.3: The student is able 1.4: The student can use system is conserved. to predict and calculate from representations and models graphical data the energy transfer to analyze situations or to or work done on an object or solve problems qualitatively system from information about and quantitatively. a force exerted on the object or system through a distance. 2.2: The student can apply mathematical routines to quantities that describe natural phenomena.

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rotational inertia rotational total angular angular total

the rotational

Return to Table of Contents Table to Return Multiple-Choice Questions

Science Practice make claims 6.4: The student can make natural about and predictions phenomena based on scientific theories and models. on a circular platform of of platform a circular on M Learning Objective The student is able to 5.E.1.1: The student is able predictions qualitative make about the angular momentum of in which a situation for a system torque. is no net external there AP Physics 1: Algebra-Based AP Physics

that is rotating counterclockwise. Assume the platform rotates without without rotates the platform Assume counterclockwise. rotating is that M inertia of the system. inertia of The child moves toward the center of the platform, increasing the increasing platform, of the center the toward moves child The momentum of the system. of momentum of the system. of The child moves toward the center of the platform, decreasing the decreasing platform, of the center the toward moves child The the increasing platform, of the center the from away moves child The decreasing platform, of the center the from away moves child The momentum of the system. of momentum

friction. Which of the following describes an action by the child that will increase the will the increase that thechild describes by action an the following of friction. Which why? reason the correct gives and system the speed platform-child of angular mass 2 (B) (C) (D) The diagram above shows a top view of a child of mass mass of child of a view top a shows above diagram The (A)

Course and Exam Description and Exam Course Enduring Understanding 5.E: The angular momentum of a is conserved. system 2. 73 Multiple-Choice Questions

3. The figure above shows the forces exerted on a block that is sliding on a horizontal surface: the gravitational force of 40 N, the 40 N normal force exerted by the surface, and a frictional force exerted to the left. The coefficient of friction between the block and the surface is 0.20. The acceleration of the block is most nearly (A) (B) (C) (D)

Enduring Understandings Learning Objectives Science Practices Sample Questions 2.B: A gravitational field is 2.B.1.1: The student is able to 1.4: The student can use ! ! caused by an object with mass. apply F = mg to calculate the representations and models gravitational force on an object to analyze situations or 3.A: All forces share certain with mass m in a gravitational solve problems qualitatively common characteristics when field of strength g in the context and quantitatively. considered by observers in of the effects of a net force inertial reference frames. 1.5: The student can reexpress on objects and systems. key elements of natural 3.B: Classically, the acceleration 3.A.1.1: The student is able to phenomena across multiple of an object interacting with express the motion of an object representations in the domain. other objects can be predicted using narrative, mathematical, 2.2: The student c an apply and graphical representations. by using . mathematical routines to 3.B.1.3: The student is able to quantities that describe reexpress a free-body diagram natural phenomena. representation into a mathematical 7.2: The student can connect representation and solve the concepts in and across domain(s) mathematical representation for to generalize or extrapolate the acceleration of the object. in and/or across enduring 3.B.2.1: The student is able to understandings and/or big ideas. create and use free-body diagrams to analyze physical situations to solve problems with motion qualitatively and quantitatively.

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Science Practice 5.1: The student can to identify analyze data or relationships. patterns Learning Objectives The student is able to The student is able 3.F.2.2: and analysis collection plan data the designed to test strategies a torque between relationship on an object and the exerted of in angular velocity change that object about an axis. to The student is able 4.B.1.2: in to find the data change analyze a constant- linear momentum for using the product mass system of the in mass and the change of mass. of the center velocity AP Physics 1: Algebra-Based AP Physics

. Another student wants to calculate the assembly’s angular speed and speed and angular the assembly’s calculate to wants student . Another t Angular only speed only in linear momentum Change Angular in linear momentum change speed and canthe graph. using be determined these quantities of Neither

(A) (B) (C) (D) A student on another planet has two identical spheres, each of mass 0.6 kg, attached to the the to 0.6 kg, attached mass of each spheres, identical two has planet another on A student vertical in the rotation a assembly the gives student The mass. negligible of a rod of ends the record Sensors above. figure in the top falls, shown so as it it then releases and plane velocity of in the graph shown is the data and spheres, the two of vertical velocity function of time function of the change in the linear momentum of the center of mass of the assembly between 0 s and between and 0 s theassembly of mass of the center of momentum in the linear the change the graph? be can using determined these quantities of 0.3 s. Which

Course and Exam Description and Exam Course Enduring Understandings on an object exerted 3.F: A force can cause a torque on that object. with other objects Interactions 4.B: the total can change or systems linear momentum of a system. 4. 75 Multiple-Choice Questions

5. A block of known mass hanging from an ideal spring of known spring constant is oscillating vertically. A motion detector records the position, velocity, and acceleration of the block as a function of time. Which of the following indicates the measured quantities that are sufficient to determine whether the net force exerted on the block equals the vector sum of the individual forces? (A) Acceleration only (B) Acceleration and position only (C) Acceleration and velocity only (D) Acceleration, position, and velocity

Enduring Understanding Learning Objectives Science Practice

Sample Questions 3.B: Classically, the acceleration 3.B.1.2: The student is able 5.1: The student can of an object interacting with to design a plan to collect and analyze data to identify other objects can be predicted analyze data for motion (static, patterns or relationships. constant, or accelerating) from by using . force measurements and carry out an analysis to determine the relationship between the net force and the vector sum of the individual forces.

3.B.3.3: The student can analyze data to identify qualitative or quantitative relationships between given values and variables (i.e., force, displacement, acceleration, velocity, period of motion, frequency, spring constant, string length, mass) associated with objects in oscillatory motion to use that data to determine the value of an unknown.

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takes to reach the floor. The The the floor. reach takes to Science Practices 4.2: The student can design data collecting a plan for a particular to answer scientific question. 6.4: The student can make about claims and predictions phenomena based on natural scientific theories and models. A the two-block system after it is is it after system the two-block falls to reach the floor the reach to falls A falls to reach the floor, and the radius of of and radius the the floor, falls reach to time block block time

A the following measurements to determine the mass of of the mass determine to measurements the following from the motion of of the motion from

B falls to reach the floor falls reach to and the distance block block distance the and A Learning Objectives The student is able 3.A.1.2: The student is able to design an experimental of the investigation motion of an object. 4.A.2.1: The student is able about the predictions to make based on the motion of a system is equal to that acceleration fact per unit in velocity the change is equal to the time, and velocity in position per unit time. change A AP Physics 1: Algebra-Based AP Physics , the distance block block , the distance

A . hangs from a light string that passes over a light pulley and is attached to to attached is pulley and a light passes over that string a light from hangs , which is on a level horizontal frictionless table, as shown above. Students are are Students above. shown as frictionless table, horizontal a level on , which is ? A B B the pulley Only the mass of block A block of the mass Only block the distance Only Only the mass of block block of mass the Only block of mass The

to determine the mass of block block of the mass determine to block block students must also take which of also takewhich must students block released from rest. They plan to measure the measure to plan They rest. from released (C) (D) (A) (B) Block

Course and Exam Description and Exam Course All forces share certain share 3.A: All forces when common characteristics in observers by considered frames. inertial reference of the 4.A: The acceleration is of mass of a system center exerted to the net force related where on the system, Enduring Understandings 6. 77 Multiple-Choice Questions

7. Two objects are released from rest at the top of ramps with the same dimensions, as shown in the figure above. The sphere rolls down one ramp without slipping. The small block slides down the other ramp without friction. Which object reaches the bottom of its ramp first, and why? (A) The sphere, because it gains rotational kinetic energy, but the block does not (B) The sphere, because it gains mechanical energy due to the torque exerted on it, but the block does not (C) The block, because it does not lose mechanical energy due to friction, but the sphere does (D) The block, because it does not gain rotational kinetic energy, but the sphere does

Enduring Understanding Learning Objectives Science Practices

Sample Questions 5.B: The energy of a 5.B.4.2: The student is able to 1.4: The student can use system is conserved. calculate changes in kinetic representations and models energy and potential energy of a to analyze situations or system using information from solve problems qualitatively representations of that system. and quantitatively.

5.B.5.4: The student is able 6.4: The student can make to make claims about the claims and predictions about interaction between a system natural phenomena based on and its environment in which scientific theories and models. the environment exerts a force on the system, thus doing work on the system and changing the energy of the system (kinetic energy plus potential energy).

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Return to Table of Contents Table to Return Multiple-Choice Questions

Science Practices 1.4: The student can use and models representations or situations to analyze qualitatively problems solve and quantitatively. 1.5: The student can reexpress key elements phenomena of natural in multiple representations across the domain. the greatest average power provided to it between it to provided power average the greatest , are initially at rest on a horizontal frictionless surface. surface. frictionless a horizontal on rest initiallyare , at m Learning Objectives The student is able to 3.A.1.1: The student is able the of an object motion express mathematical, using narrative, representations. and graphical to 3.E.1.4: The student is able to routines mathematical apply in kinetic the change determine the of an object given energy on the object and the forces displacement of the object. AP Physics 1: Algebra-Based AP Physics m

and 2 m m . Which block has has block . Which ? t . m is exerted individually on each block, as shown above. The graph shows how how shows The graph above. as shown block, each on individually exerted is F and

mass The block of mass 2 mass of block The them. to provided power the same have Both blocks the maximum of the ratio knowing without be determined cannot It The block of mass mass of block The

(A) (B) (C) (D) Two blocks, of mass mass of blocks, Two A force A force varies varies with time

Course and Exam Description and Exam Course Enduring Understandings certain share 3.A: All forces when common characteristics in observers by considered frames. inertial reference on an object exerted 3.E: A force of the kinetic energy can change the object. 8. 79 Multiple-Choice Questions

Enduring Understandings Learning Objectives Science Practices

5.B: The energy of a 5.B.5.3: The student is able 2.2: The student can apply system is conserved. to predict and calculate from mathematical routines to graphical data the energy transfer quantities that describe natural to or work done on an object or phenomena. system from information about 6.4: The student can make a force exerted on the object or claims and predictions about system through a distance. natural phenomena based on 5.B.5.5: The student is able scientific theories and models. to predict and calculate the energy transfer to (i.e., the work done on) an object or system from information about a force exerted on the object or system through a distance. Sample Questions

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A the moon is

moon on the planet

the moon speedhas the moon

Return to Table of Contents Table to Return Multiple-Choice Questions B

Science Practices make 6.4: The student can make about claims and predictions phenomena based on natural scientific theories and models. 7.2: The student can connect in and across concepts or domain(s) to generalize in and/or across extrapolate enduring understandings and/or big ideas. planet on the moon on planet

for determining the distance of the the determining of the distance for

terms of the given quantities? the given of terms from the planet. At point point At planet. the from

in B Learning Objectives The student is able The student is able 5.B.5.4: claims about the to make a system between interaction in which and its environment a force exerts the environment thus doing work on the system, and changing the on the system (kinetic of the system energy energy). plus potential energy to 5.E.1.1: The student is able predictions qualitative make about the angular momentum of in which a situation for a system torque. is no net external there AP Physics 1: Algebra-Based AP Physics

and is at distance distance at is and is the same as that exerted by the planet on the moon the on planet the by exerted that as same the is moon on the planet is the same as that exerted by the by exerted asthat the same is the planet on moon the planet directed toward always is moon Conservation of angular momentum, because the gravitational force the gravitational because angularof momentum, Conservation Conservation of angular momentum, because the gravitational force the gravitational because angularof momentum, Conservation on exerted force the gravitational because energy, of Conservation the by exerted force gravitational the because energy, of Conservation always directed toward the planet directed toward always

has speed speed has Which of the following explains a correct method correct a explains the following of Which (B) (C) (D) (A) A moon is in an elliptical orbit about a planet as shown above. At point point At above. asshown a planet about inis an elliptical orbit A moon moon from the planet at point point at the planet from moon

Course and Exam Description and Exam Course Enduring Understandings of a The energy 5.B: is conserved. system 5.E: The angular momentum is conserved. of a system 9. 81 Multiple-Choice Questions

Questions 10 –12 refer to the following material.

Block 1 of mass and block 2 of mass are sliding along the same line on a horizontal frictionless surface when they collide at time . The graph above shows the velocities of the blocks as a function of time.

10. Which block has the greater mass, and what information indicates this? (A) Block 1, because it had a greater speed before the collision. (B) Block 1, because the velocity after the collision is in the same direction as its velocity before the collision. (C) Block 2, because it had a smaller speed before the collision. (D) Block 2, because the final velocity is closer to the initial velocity of block 2 than it is to Sample Questions the initial velocity of block 1.

Enduring Understandings Learning Objectives Science Practices

4.A: The acceleration of the 4.A.2.3: The student is able to 1.4: The student can use center of mass of a system is create mathematical models and representations and models related to the net force exerted analyze graphical relationships to analyze situations or for acceleration, velocity, and solve problems qualitatively on the system, where . position of the center of mass of a and quantitatively. system and use them to calculate 2.2: The student can apply 5.D: The linear momentum properties of the motion of the mathematical routines to of a system is conserved. center of mass of a system. quantities that describe 5.D.2.5: The student is able to natural phenomena. classify a given collision situation as elastic or inelastic, justify the selection of conservation of linear momentum as the appropriate solution method for an inelastic collision, recognize that there is a common final velocity for the colliding objects in the totally inelastic case, solve for missing variables, and calculate their values.

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before the collision, the collision, before collision, and there there and collision,

collision, so some of their their of so some collision, Return to Table of Contents Table to Return Multiple-Choice Questions

Learning Objective The student is able The student is able 5.D.2.3: of the conservation to apply linear momentum to a closed in of objects involved system an inelastic collision to predict in kinetic energy. the change AP Physics 1: Algebra-Based AP Physics

during the collision negligible. is the collision during kinetic energy was transformed into kinetic energy was transformed so some of their kinetic their energy cancels. of so some is no friction acting on them. acting friction no on is It is less, because the blocks have the same velocity after after the velocity same the have blocks the because less, is It directions in opposite velocities have the blocks because less, is It so the effect was instantaneous, the collision because the same, is It after the velocity the same have the blocks because the is same, It

kinetic energy before the collision, and why? and the collision, kinetic energy before (D) (B) (C) How does the kinetic energy of the two-block system after collision after the system the two-block the kineticdoes energy of How (A)

Course and Exam Description and Exam Course Enduring Understanding 5.D: The linear momentum is conserved. of a system 11. 83 Multiple-Choice Questions

12. Which of the following is true of the motion of the center of mass of the two-block system during the time shown? (A) The center of mass does not move because the blocks are moving in opposite directions before the collision. (B) The center of mass moves at a constant velocity of because there is no friction acting on the system. (C) The center-of-mass velocity starts out greater than but decreases to during the collision because the collision is inelastic. (D) The center-of-mass velocity increases as the blocks get closer together, and then becomes constant after the collision.

Enduring Understanding Learning Objective Science Practices

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acceleration of the the of acceleration

Return to Table of Contents Table to Return Multiple-Choice Questions as a function of time of asa function

Science Practices reexpress 1.5: The student can reexpress key elements of natural multiple phenomena across in the domain. representations 2.2: The student can apply to routines mathematical quantities that describe phenomena. natural divide the graph into four sections. four into the graph divide

Learning Objectives The student is able to 3.A.1.1: The student is able the of an object motion express mathematical, using narrative, representations. and graphical 3.A.1.3: The student is able experimental data to analyze describing the motion of an to express object and is able using of the analysis the results and mathematical, narrative, representations. graphical AP Physics 1: Algebra-Based AP Physics

(C) (D) Which of the following correctly ranks the magnitude of the average ranks of correctly the magnitude the following of Which (A) (B) A cart is constrained to move along a straight line. A varying line. a straight along force net move A cart to is constrained Questions 13 –15 refer to the following to information. –15 refer Questions 13 direction of motion is exerted on the cart. The cart’s velocity velocity the cart. on The exerted is cart’s motion of direction cart during the four sections of the graph? of sections cart the four during shown in the graph above. The five labeled points labeled five The above. ingraph the shown

Course and Exam Description and Exam Course Enduring Understanding certain share 3.A: All forces when common characteristics in observers by considered frames. inertial reference 13. 85 Multiple-Choice Questions

14. For which segment does the cart move the greatest distance? (A) AB (B) BC (C) CD (D) DE

Enduring Understanding Learning Objective Science Practices

2.2: The student can apply mathematical routines to quantities that describe natural phenomena. Sample Questions

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Science Practices 1.4: The student can use and models representations or situations to analyze qualitatively problems solve and quantitatively. 2.2: The student can apply to routines mathematical quantities that describe phenomena. natural 6.4: The student can make about claims and predictions phenomena based on natural scientific theories and models. 7.2: The student can connect concepts or extrapolate to generalize enduring in and/or across and/or big ideas. understandings Learning Objectives The student is able to 3.E.1.3: The student is able vectors and velocity use force or qualitatively to determine exerted the net force quantitatively on an object and qualitatively of that whether kinetic energy decrease, increase, object would unchanged. or remain The student is able 5.B.5.4: claims about the to make a system between interaction in which and its environment a force exerts the environment thus doing work on the system, and changing the on the system (kinetic of the system energy energy). plus potential energy AP Physics 1: Algebra-Based AP Physics

The speed isThe decreasing. is positive. acceleration The negative. is acceleration The The speed The is increasing.

(B) (C) (D) During some part of the motion, the work done on the cart is negative. What feature of of feature What the cart on negative. is done the work part the motion, During of some the motion indicatesthis? (A)

Course and Exam Description and Exam Course A force exerted on an exerted 3.E: A force the kinetic object can change of the object. energy of a The energy 5.B: is conserved. system Enduring Understandings 15. 87 Multiple-Choice Questions

16. The figure above shows a block on a horizontal surface attached to two springs whose other ends are fixed to walls. A light string attached to one side of the block initially lies straight across the surface, as shown. The other end of the string is free to move. There is significant friction between the block and the surface but negligible friction between the string and the surface. The block is displaced a distanced and released from rest. Which of the following best represents the shape of the string a short time later? Sample Questions

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Science Practices The student can use 1.4: The student and models representations or situations to analyze qualitatively problems solve and quantitatively. 6.4: The student can make about claims and predictions based on phenomena natural scientific and models. theories 7.2: The student can connect domain(s) in and across concepts or extrapolate to generalize enduring in and/or across and/or big ideas. understandings Learning Objectives Learning The student is able is able The student 3.B.3.1: which properties to predict the a motion of determine and harmonic oscillator simple thewhat dependence of the motion is on those properties. The student is able 4.C.2.1: about the predictions to make in the mechanical changes when a of a system energy force component of an external to or antiparallel acts parallel of the displacement the direction of mass. of the center to 6.A.3.1: The student is able representation use graphical of a periodic mechanical the to determine wave amplitude of the wave. AP Physics 1: Algebra-Based AP Physics

. Course and Exam Description and Exam Course Interactions with other Interactions 4.C: can change objects or systems of a system. the total energy is a traveling 6.A: A wave disturbance that transfers and momentum. energy Enduring Understandings Enduring the acceleration Classically, 3.B: with interacting of an object other be predicted objects can using by 89 Multiple-Choice Questions

17. Two massive, positively charged particles are initially held a fixed distance apart. When they are moved farther apart, the magnitude of their mutual gravitational force changes by a factor of n. Which of the following indicates the factor by which the magnitude of their mutual electrostatic force changes? (A) (B) (C) n (D)

Enduring Understanding Learning Objectives Science Practices

3.C: At the macroscopic level, 3.C.2.1: The student is able to 6.4: The student can make forces can be categorized as use Coulomb’s law qualitatively claims and predictions about either long-range (action-at-a- and quantitatively to make natural phenomena based on distance) forces or contact forces. predictions about the interaction scientific theories and models. between two electric point 7.2: The student can connect charges (interactions between concepts in and across domain(s) collections of electric point to generalize or extrapolate charges are not covered in in and/or across enduring Physics 1 and instead are understandings and/or big ideas. restricted to Physics 2). 3.C.2.2: The student is able to connect the concepts of gravitational force and electric force to compare similarities and

Sample Questions differences between the forces.

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R a function of time. Which

for the resistance? larger for

AP Physics 1: Algebra-Based AP Physics

dissipated by the smaller by as resistance dissipated E of the following shows the corresponding graph the corresponding the shows of following The circuit shown above contains two resistors of resistance resistance of resistors two contains above shown circuit The the total energy

Course and Exam Description and Exam Course 18. 91 Multiple-Choice Questions

Enduring Understanding Learning Objectives Science Practices

5.B: The energy of a 5.B.9.1: The student is able to 1.1: The student can create system is conserved. construct or interpret a graph representations and models of of the energy changes within natural or man-made phenomena an electrical circuit with only a and systems in the domain. single battery and resistors in 1.4: The student can use series and/or in, at most, one representations and models parallel branch as an application to analyze situations or of the conservation of energy solve problems qualitatively (Kirchhoff’s loop rule). and quantitatively. 5.B.9.3: The student is able to 6.4: The student can make apply conservation of energy claims and predictions about (Kirchhoff’s loop rule) in natural phenomena based on calculations involving the total scientific theories and models. electric potential difference for complete circuit loops 7.2: The student can connect with only a single battery and concepts in and across domain(s) resistors in series and/or in, to generalize or extrapolate at most, one parallel branch. in and/or across enduring understandings and/or big ideas. Sample Questions

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Science Practice 2.2: The student can apply to routines mathematical quantities that describe phenomena. natural . The student then moves the oscillator to to oscillator the moves then student . The 0 wave with one antinode is formed on the string on formed is antinode with one wave f

Learning Objective The student is able The student is able 6.D.4.2: and wavelengths to calculate speed) wave (if given frequencies based on of standing waves boundary conditions and length within which the of region calculate is confined, and wave of wavelengths values numerical Examples and frequencies. include musical instruments. AP Physics 1: Algebra-Based AP Physics the oscillator is is the oscillator

horizontal segment of string to half its original length. At what frequency what originalhalf string length.At to its of segment horizontal

0 f There is no frequency at which a standing wave willformed. be standing wave a at which no is frequency There

) C end of the string is passed over a pulley and attached to a suspended weight, as shown as shown weight, a suspended to attached pulley a and the string passed is of over end standing a finds that student The above. (B) ( (D) A student connects one end of a string with negligible mass to an to mass a string of with negligible end one connects A student shorten the the string? on be formed now antinode with one will wave a standing (A) when the frequencyof

Course and Exam Description and Exam Course Enduring Understanding and 6.D: Interference to superposition lead and beats. standing waves 19. 93 Multiple-Choice Questions

20. The figure above shows a portion of a periodic wave on a string at a particular moment in time. The vertical arrows indicate the direction of the velocity of some points on the string. Is the wave moving to the right or to the left? (A) To the right (B) To the left (C) Neither direction; the wave is a standing wave, so it is not moving. (D) Either direction; the figure is consistent with wave motion to the right or to the left.

Enduring Understanding Learning Objective Science Practice

6.A: A wave is a traveling 6.A.1.2: The student is able 1.2: The student can describe disturbance that transfers to describe representations representations and models of energy and momentum. of transverse and natural or man-made phenomena longitudinal waves. and systems in the domain. Sample Questions

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Science Practices reexpress 1.5: The student can reexpress key elements of natural multiple phenomena across in the domain. representations 6.4: The student can make about claims and predictions phenomena based on natural scientific theories and models. 7.2: The student can connect domain(s) in and across concepts or extrapolate to generalize enduring in and/oracross and/or big ideas. understandings Which of the following

must increase? must

Learning Objectives 3.A.1.1: The student is able to 3.A.1.1: The student is able the motion of an object express mathematical, using narrative, representations. and graphical 6.A.2.1: The student is able to describe sound in terms and of energy of transfer momentum in a medium and the concepts to everyday relate examples. AP Physics 1: Algebra-Based AP Physics

Both the maximum displacement and the average speed average the and Boththe maximum displacement The maximum displacement only maximum The displacement only speed average The Neither the maximum displacement nor the average speed the average nor the maximum displacement Neither

) C shown above. A person turns up the volume on the radio. on the volume turns up A person above. shown ( (D) (A) (B) A radio speaker produces sound when a membrane called diaphragm a a membrane when sound speaker produces A radio aspects of the motion of a point on the diaphragm on a point of aspects the motion of

Course and Exam Description and Exam Course Enduring Understandings certain share 3.A: All forces when common characteristics in observers by considered frames. inertial reference is a traveling 6.A: A wave energy disturbance that transfers and momentum. 21. 95 Multiple-Choice Questions

Directions: For each of questions 22–25 below, two of the suggested answers will be correct. Select the two answers that are best in each case, and then fill in both of the corresponding circles on the answer sheet.

22. A block is given a short push and then slides with constant friction across a horizontal floor. The graph above shows the kinetic energy of the block after the push ends as a function of an unidentified quantity. The quantity could be which of the following? Select two answers. (A) Time elapsed since the push (B) Distance traveled by the block (C) Speed of the block (D) Magnitude of the net work done on the block

Sample Questions Enduring Understandings Learning Objectives Science Practices

3.A: All forces share certain 3.A.1.1: The student is able to 1.5: The student can reexpress common characteristics when express the motion of an object key elements of natural phenomena considered by observers in using narrative, mathematical, across multiple representations in inertial reference frames. and graphical representations. the domain. 3.E: A force exerted on an 3.E.1.1: The student is able 2.2: The student can apply object can change the kinetic to make predictions about the mathematical routines to energy of the object. changes in kinetic energy of an quantities that describe natural object based on considerations of phenomena. the direction of the net force on 6.4: The student can make claims the object as the object moves. and predictions about natural phenomena based on scientific theories and models. 7.2: The student can connect concepts in and across domain(s) to generalize or extrapolate in and/or across enduring understandings and/or big ideas.

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Return to Table of Contents Table to Return Multiple-Choice Questions

Science Practices 1.2: The student can describe and models of representations phenomena or man-made natural in the domain. and systems 6.4: The student can make about claims and predictions phenomena based on natural scientific theories and models. media? Select two answers. Select two media?

Learning Objectives The student is able to The student is able 6.D.3.2: of standing properties predict the addition from that result waves waves of incident and reflected region and confined to a that are nodes and antinodes. have to The student is able 6.D.3.4: and describe representations in which models of situations the from result standing waves addition of incident and reflected region. a confined to waves AP Physics 1: Algebra-Based AP Physics

The stringThe guitar guitar the The air inside guitar the surrounding The air musician the beneath The ground

waves will the following occur likely of in which most waves (B) (C) (D) A musician stands outside in a field and plucks a string on an acoustic an on string a plucks and a field in outside stands musician A (A)

Course and Exam Description and Exam Course Interference and and 6.D: Interference to superposition lead and beats. standing waves Enduring Understanding 23. 97 Multiple-Choice Questions

24. A 0.2 kg rock is dropped into a lake from a few meters above the surface of the water. The rock reaches terminal velocity in the lake after 5 s in the water. During the final 3 s of its descent to the lake bottom, the rock moves at a constant speed of 4 m/s. Which of the following can be determined from the information given? Select two answers. (A) The speed of the rock as it enters the lake (B) The distance the rock travels in the first 5 s of its descent in the water (C) The acceleration of the rock 2 s before it reaches the lake bottom (D) The change in potential energy of the rock-Earth-water system during the final 3 s of the rock’ s descent

Enduring Understandings Learning Objectives Science Practices

3.A: All forces share certain 3.A.1.1: The student is able to 1.5: The student can reexpress common characteristics when express the motion of an object key elements of natural considered by observers in using narrative, mathematical, phenomena across multiple inertial reference frames. and graphical representations. representations in the domain. 4.C: Interactions with other 4.C.1.2: The student is able 6.4: The student can make objects or systems can change to predict changes in the claims and predictions about the total energy of a system. total energy of a system due natural phenomena based on to changes in position and scientific theories and models. speed of objects or frictional interactions within the system. Sample Questions

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Return to and

Science Practices make 6.4: The student can make about claims and predictions phenomena based on natural scientific theories and models. 7.2: The student can connect domain(s) in and across concepts or extrapolate to generalize enduring in and/or across and/or big ideas. understandings , respectively. Later, all three all three Later, , respectively. e 3 − , and , and e 5 Learning Objectives The student is able to The student is able 1.B.1.2: using the predictions, make charge, of electric conservation about the sign and relative of objects quantity of net charge charging various after or systems including conservation processes, circuits. in simple of charge to The student is able 1.B.3.1: the claim that an electric challenge than smaller the elementary charge has been isolated. charge + AP Physics 1: Algebra-Based AP Physics , e

3 + Z +5e +4.5e +7e −7e Y −4e +4.5e −8e +6e X +4e +4e +5e +6e simultaneously and then separate. Which of the following are following the of Which separate. then and simultaneously In an experiment, three microscopic latex spheres are sprayed into a chamber into sprayed are spheres latex microscopic three experiment, an In final charges on the spheres? Select two answers. two Select spheres? on the charges final become charged with with charged become

(B) (C) (D) (A) Course and Exam Description and Exam Course 25. Electric charge is a property is a property charge Electric 1.B: affects that system or object an of with other objects its interactions containing charge. or systems Enduring Understanding 99 100 Sample Questions Answers Questions to Multiple-Choice 13. D 12. B 11. A 10. D 9. B 8. A 7. D 6. C 5. B 4. C 3. D 2. B 1. A Answers Questions to Multiple-Choice AP Physics 1:Algebra-Based

Course andExam Description

Sample Questions 101

Return to are

You may include include may You

Free-Response Questions Free-Response Return to Table of Contents Table to Return speaker connected to a a to speakerconnected

Science Practices 1.2: The student can describe and models of representations or man–made phenomena natural in the domain. and systems 6.1: The student can justify claims with evidence. 6.4: The student can make about claims and predictions phenomena based on natural scientific theories and models. frequency and then turned on. The frequency is then is then The frequency on. turned then and frequency

Learning Objectives The student is able to The student is able 6.D.3.2: of standing properties predict the addition from that result waves waves of incident and reflected region and confined to a that are nodes and antinodes. have to The student is able 6.D.3.4: and describe representations in which models of situations the from result standing waves addition of incident and reflected region. confined to a waves to The student is able 6.D.4.1: with the evidence challenge of claim that the wavelengths determined are standing waves of the source the frequency by of the size of the region. regardless AP Physics 1: Algebra-Based AP Physics

produce resonances in the tubes. Students observe that at first only firstonly at that observe inStudents the tubes. resonances produce

Question 1 is a short free-response question that requires about 12 minutes to to 12 minutes about that question requires 1 is a short Question free-response the tubes resonates at a time. Later, as the frequency gets very high, there gets as the frequency a time. Later, at the tubes resonates

times when both tubes resonate. both times when some are there explain why answer, paragraph-length coherent, a clear, In slowly increased to increased slowly frequencies, but no low frequencies, at which both tubes resonate. both tubes which at frequencies, low no but frequencies, one of The figure above shows two tubes that are identical except for their slightly their for except identical are tubes two that shows above figure The lengths. Both tubes have one open end and one closed end. A end. closed one and end open one Bothlengths. tubes have variable frequency generator is placed in front of the tubes, as shown. The speaker is is speaker The shown. as tubes, the of in front placed is generator frequency variable very low of note a produce set to diagrams and/or equations as part of your explanation. aspart your of equations diagramsand/or

Course and Exam Description and Exam Course Enduring Understanding and 6.D: Interference to superposition lead and beats. standing waves 1. Free-Response QuestionsFree-Response Directions: answer and is worth 7 points. Questions 2 and 3 are long free-response questions that require that questions require free-response long and 3 are Questions 2 worth and is 7 points. answer each part for work worth your 12 points each. Show and are each to answer about 25 minutes that part. after in the space provided 101 102 Sample Questions Free-Response Questions 2. AP Physics 1:Algebra-Based

A groupA of students has two carts, (c) (b) (a) cart cart of mass cart the to determine mass mass travel can friction.carts Thealong a straight horizontalCart track.

may includeoflabeled a diagram before andthe after collision. For your Given in the calculated value of calculated mass the of the cart in A groupA of students took measurements for one collision. Agraphof the measurements beforethe taken after collision or the taken by those sourcesbe There will of errorthe in measurementsin taken that so anotherdetail student out could your carry procedure. experimental an Describe procedure to determine velocities the of data is shown below. the principles the your in used calculations. what measurements what and after acollision,theincluding additionalall will it be equally affected by both sets sets of measurements?both by affected it equally be will B is initially at rest, is initially . The. studentsare asked a use to one-

, use the graph the use , to massthe of calculate cart

you would andhow take youwould them. Include take enough

as shownstick together.as above.carts thethe collision, After Course andExam Description B . Before the collision, cart Beforecollision, cart the A and and

your setup to help your in description. Indicate B

, with wheels, with that with turn experimental procedure, uncertaintythe will B dimensional collision between the carts carts collisiondimensional the between be affected moreaffected be theby errorthein

equipment you wouldneed. You A

Justify youranswer. Justify travels andright to the Return to Table ofContents

the experiment,the both B A .

Explicitly indicate indicate Explicitly has known known has

the carts before carts the negligible negligible

students’

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Sample Questions 103

use (but do not not do use (but

Free-Response Questions Free-Response Return to Table of Contents Table to Return

Science Practices 4.2: The student can design a to answer data collecting plan for a particular scientific question. 5.1: The student can to identify analyze data or relationships. patterns 5.3: The student can evaluate data by provided the evidence to a particular sets in relation scientific question. of the physical quantities quantities the physical of

dissipated in the collision. How could you you could How in the collision. dissipated

to investigate this question? Be sure to explicitly describe the explicitly to Be sure this question? investigate to

Learning Objectives The student is able 3.A.1.2: The student is able to design an experimental of the investigation motion of an object. to The student is able 5.D.1.4: of design an experimental test of the an application principle of linear of the conservation an outcome of momentum, predict the experiment using the principle, that by generated data analyze experiment whose uncertainties and numerically, expressed are the the between match evaluate and the outcome. prediction to plan The student is able 5.D.2.2: the to test strategies collection data of momentum of conservation law that collision is in a two-object elastic or inelastic and analyze graphically. data the resulting AP Physics 1: Algebra-Based AP Physics

collision, specifically whether the initial values of one specificallyof initialthe collision, whether values actually do any algebra or arithmetic). or algebra actuallyany do calculations you would make, specifying all equations you would make,specifying you would allyou calculations equations modify the experiment affect the fraction of mechanicalenergyaffectof the fraction The students are now asked to consider energychanges the kinetic to consider asked now are students The

(d) Course and Exam Description and Exam Course Enduring Understandings certain share 3.A: All forces when common characteristics in observers by considered frames. inertial reference 5.D: The linear momentum is conserved. of a system 103 104 Sample Questions Free-Response Questions AP Physics 1:Algebra-Based 3.

maximum speed same the reach to section straight ofeach for one-fourth acceleration at constant to speed speed to Car Car spaced (c) (b) (a) speed to return to sections semicircular with aracetrack represents above figure The brakes at constant acceleration for the other half of each straight of each half other for the acceleration at constant brakes acceleration straight sections. Each section has length length has section Each sections. straight brakes at brakes

label dot the 0. with terms your in equations Onbelow, figuresthe draw arrowan showingthedirection theof Explain howExplain your equations (b) part in reexpress ii your reasoning i. not simply refer to results any final of your of at cars the positionsthe noted by dots.the If the ii. X

goes around the around goes track in lesstrack in quantitatively time appropriate with and justify yourand justify answer qualitatively without using Justify Justify your answer about which car, either, if completes one trip Indicatewhich car, either, if completes onetrip around track the

constant acceleration for the remaining fourth of each straight section straight of each fourth remaining for the acceleration constant

. Car . Car apart. Two cars drive apart. people

for half of each straight section to reach a maximum speed of speed amaximum reach to section straight of each for half Y also goes around the curves at curves the around goes also

, stays at that speed for half of each straight section, then then section, straight of each for half speed at that stays ,

curves at constant speed speed at constant curves

Course andExam Description

correspond to concepts yourin qualitative explanation.

counterclockwise around the track, as shown. shown. as track, the around counterclockwise d , and ,

calculations, but instead indicate how indicate but instead calculations,

markers along the track are are track the along markers

constant speed speed constant

, increases speed at constant at constant speed , increases

net force is zero at anyposition,

equations.

equations. Return to Table ofContents

section to return return to section

connected by

, increases speed speed , increases net force on each

in part (b) part in i. Do

around the the around

then then Return to

Sample Questions 105

Return to to

or man-made phenomena

Free-Response Questions Free-Response Return to Table of Contents Table to Return The student can apply student The The student can can student The create create can student The

Science Practices and systems in the in domain. and systems 1.1: 1.1: and models of representations natural 1.5: elements of natural key multiple phenomena across representations 2.2: routines mathematical quantities that natural phenomena. natural

The student is able to able is student The The student is able to is able student The Learning Objectives Learning 3.A.2.1: in diagrams forces represent 3.A.1.1: 3.A.1.1: thean object motion of express mathematical, using narrative, representations. and graphical using or mathematically with vectors labeled appropriately and units direction, magnitude, situation. of a during theanalysis AP Physics 1: Algebra-Based AP Physics

Course and Exam Description and Exam Course Enduring Understanding Enduring certain share 3.A: All forces when common characteristics in observers by considered frames. inertial reference 105 106 Sample Questions Scoring Guidelines Scoring Guidelines AP Physics 1:Algebra-Based wavelength of sound, the as shown below. In order to resonate, length the of atube must anmultiple be odd of aquarter Example: length, explaining how tubes both can now conditions boundary meet atoccurs atime wavelengths at low to frequency) explain why only one resonance For above the linking two (conditions ideas of resonance and comparing For comparing wavelengths at lengths to tube the low frequency Explanations can include figures to the meaning support or clarify Scoring Guidelinesfor Free-Response Question1(7points) For indicating how wavelengths smaller relate to differences in tube For indicating that up, goes as frequency wavelength down goes For explaining conditionthe for at resonanceclosed a tube in alone are not sufficient. wavelengths other the contains while 19quarter wavelengths. wavelength at same the —for time instance, one tube might contain 17quarter tubesthe can contain an multiple odd of quarter wavelengths for same the When wavelength the half becomes of order the of difference the in lengths, tube increases, wavelength the and decreases many more wavelengths fit inside a tube. difference in lengthstube is than much wavelength. a smaller half frequency the As length match of the tubes. the So for can occur only one tube at —the atime For resonance at low frequencies, wavelength the of sound the is of order the of the

Course andExam Description

one end one Return to Table ofContents

of prose, but figures

Sample Questions 107

if the same same if the

give it an initial initial an it give

Scoring Guidelines Scoring before the collision collision the before to

to give it an initial initial an it give to A

A and then for the the for then and Return to Table of Contents Table to Return

percent error could be the be the could error percent the of magnitude the

cart

collision. Push cart cart Push collision.

. to measure the time it takes for the cart(s) to cross the the cross to cart(s) the for takes it time the measure to B

AP Physics 1: Algebra-Based AP Physics

and A distances. The speeds are the distances divided by the by times. the divided distances the are speeds The distances.

speed. Record position as a function of time, first for first time, of a function as position speed. Record measure with the same accuracy at the greater speed). So greater the accuracy same the at with measure speed). So greater the accuracy same the at with measure motion detector is is usedthroughout. detector motion Measurement error could be greater before the collision (it could be could (it collision the before be greater could error Measurement be could (it collision the before be greater could error Measurement collision the after and before be same the could error Measurement Place a motion detector at the left end of the track. Push cart cart Push of track. the left the end at detector Place a motion points) (2 (3 points) cart for one — on track the distances two off mark to tape Use and one for the combined carts after the after carts combined the for one and greater. or same be the same. could uncertainty reported marked speed. Use a stopwatch speed. Use combined carts carts combined

n n n (b) size the relative about assumption a reasonable indicating For on the the effect in comparing the assumption using correctly For n For indicating all the measurements needed the velocities determine to all the measurements indicating For measurements or equipment extraneous obviously no having For Examples: n Scoring Guidelines for Free-Response Question 2 (12 points) Question 2 Free-Response Guidelines for Scoring (a) useful allow measurements would that setup a reasonable For calculated value of the mass of cart B of the mass of calculated value Example: effect a greater they will have magnitude, the same of are errors the measurement If carts will the initial combined speed than be less of The ofthe speed collision. the after the actual value of percentage will be a greater magnitude the same of cart A, so errors value oneffect the greater a have will collision the after So values collision. the the after cart B. of the mass of the following: of any also could argue A response of the measurement errors before and after collision the after and before errors the measurement of Course and Exam Description and Exam Course 107 108 Sample Questions Scoring Guidelines AP Physics 1:Algebra-Based The speed The speed data points not on line[s].) the one or morepoint (This speeds cannot calculationsearned if be use from slope corresponding to before and afterthe collision ofConservation momentum to determine mass used the can be of B cart throughout calculations) the calculationthe (ineither asingle explanation or dispersed (c) The speed The speed For indicating of use slope the of one or two drawn lines to determine For using data from graph the to attempt calculation of speed For correctly recognizing two the regions on graph the For providing sufficient description the of principles in used Using example the lines drawn above:

(4 points) before collision the is slope the of best-fit the line forthedata from 0 to 1s.

afterthe collision the is slope best-fitthe of line the for fromdata 1s to2s.

Course andExam Description

Return to Table ofContents

Sample Questions 109

K Scoring Guidelines Scoring

energy

Return to Table of Contents Table to Return

0 0 Car Y initial speed

. Then analyze analyze . Then indicates that the previously the previously that indicates

lost in the various collisions in the various lost K AP Physics 1: Algebra-Based AP Physics

directed toward the right, and the left one for for one the left and the right, toward directed Car X or one of the cartof masses that one OR or A equal to zero) equal to (3 points) (3 points)

I I of cart of described procedure would provide appropriate data, so it does so it not data, appropriate provide describedwould procedure need modification becan used the data calculate the to kinetic that indicating For For an answer consistent with previous responses that indicates that responses previous with consistent answer an For For correct directions of the net forces at all the locations on the on all the locations at forces the net of directions correct For on all the locations at forces the net of directions correct For the top on all locations at forces the net of directions correct For to see if the changes in initial speed give different values. in initial speed if the changes different give to see 3 (12 points) Question Free-Response GuidelinesScoring for (a) Example: kinetic of values calculate the data, vary could the initial speed cart From A. of You using collision the after and energy before before and after the collision after and before the fraction that of indicating For (d) Applying conservation of momentum: of conservation Applying car the bottom straightaways (i.e., directed toward the center of the segment) of the center toward directed (i.e., straightaways the bottom the left, toward directed arrows both rightmost (i.e., straightaway X car for one the left should beshould compared the circle) of the center toward allsemicircular sections generally directed (i.e., modification of the procedure to accomplish varying the accomplish to procedure of the modification Course and Exam Description and Exam Course 109 110 Sample Questions Scoring Guidelines AP Physics 1:Algebra-Based For realizing that difference the time in is only the on straightaways Y Y Car Car Car Car Example: straightaways Example: ittime for takes one segment of acceleration on straightaways the of of For correct reasoning leading to CarY (b) For stating that to time the is travel each curve timeThe travel to is curve each Thecalculations showthat car Y Adding three segments to get total the for time one straightaway gives timeThe forcar Y travelto one constant section the on straightaway speed is Doing calculation the shown above using distance the of acceleration for time the Calculating car Yto travel one straightaway: for time the carCalculating X For correctly straightawaytotal determining the for times thattime car Y For work that shows an understanding of how tothe determine thattime car For work that shows an understanding of how tothe determine For correct kinematics expressions that allow determination of the will use use will result that one of acceleration section atime takes cars take the same time on the curves, so car Y so ontime curves, same the the take cars

must overall ashorter take time. must cover straightaways the inashorter same the take car time. time, Curves so

ii) i) (7 (7 Y X

(2 points) or or accelerates over ashorter and time spends going time at car top So speed. takes longertakes to accelerate and not does spendany traveling time at top speed. ons total points (5 points) (5 X

and car Y spends atspends constant speed .

) . or some other unit defined time.of calculations The below

each spend accelerating spend each Course andExam Description to travel one straightaway: takes less takes on time astraightaway, and both . Answers expressed can be interms taking ashorter taking on time the overall takes lessoverall takes time. ,

each careach Return to Table ofContents

Return to 1 point 1 point 1 point 1 po 1 1 po 1 1 point 1 poin

int int t

Sample Questions 111

t t .

does, as argued in does, argued as

Return to Table of Contents Table to Return takes longer to accelerate. The accelerate. to takes longer traveling for a time at top speed. top a time at for traveling Y reaches its maximum speed more quickly quickly speed more maximum its reaches corresponds to car car to corresponds AP Physics 1: Algebra-Based AP Physics

into the displacement equation in part (b) ii gives equation the displacement into

(2 points)

and therefore spends more time at its maximum speed X car than maximum its time at more spends therefore and part (b) i. Substituting Substituting This shows that a car takes less time to reach its maximum speed when it accelerates speed it accelerates maximum when its reach to less time a takes car that shows This Y car means This distance. a shorter over For linking math to all other qualitative reasoning that explains explains that reasoning all qualitative to other linking math For (c) explains that reasoning aspect qualitative of one to linking math For equation equation the difference in times the difference in times the difference Examples: acceleration linear of one segment of forthe time inthe calculations difference only The X car that shows That in distances. the difference is Course and Exam Description and Exam Course 111 112 Appendixes that makethat material. upthe interactions atoms andmolecules ofthe resultthat from arrangement the and have many macroscopic properties Enduring Understanding 1.E:Materials satisfyand that conservation principles. experimentally verifiedthe same tobe mass andgravitational are massthat and systems have properties ofinertial Enduring Understanding 1.C: Objects charge. objectsorsystemsother containing system affects that itsinteractions with charge isaproperty ofanobjector Enduring Understanding 1.B: Electric many properties system. ofthe internal structure ofasystem determines Enduring Understanding 1.A:The Big 1: Idea Physics AP in 1 Ideas Big The A: Appendix AP Physics 1:Algebra-Based

and charge. Systems may have internal structure. structure. internal have may Systems charge. and Obj ects and systems have properties such as mass mass as such properties have systems and ects

Course andExam Description resistivity. Essential Knowledge 1.E.2:Matter hasaproperty called conservation principles. experimentallythat satisfy verifiedthe sameand tobe properties mass andgravitational ofinertial are massthat Essential Knowledge 1.C.3: Objectsandsystems have gravitational fields. gravitationalof the interaction objects, other systems, with or property ofanobjectorasystem determines that strength the Essential Knowledge 1.C.2: Gravitational massisthe when itinteracts objectsorsystems. other with an objectorasystem determines that how itsmotionchanges Essential Knowledge 1.C.1: property massisthe Inertial of elementary charge.as the charge canbeisolated that isthe electron charge, alsoknown Essential Knowledge 1.B.3: Thesmallest observed unitof of somefundamentalparticles have that noelectric charge. quantities ofpositive andnegative charge, exception the with electric charge. Neutral objectsorsystems containequal Essential Knowledge 1.B.2: There are only two kindsof system. objectsinthe of allthe The netcharge ofasystem charges sumofthe isequaltothe Essential Knowledge 1.B.1: Electric charge isconserved. system, system the itselfmay bereferred toasanobject. behavior inmodelingthe not important macroscopic ofthe Physics, properties are constituentparts whenthe ofthe constituent atomic andmolecular substructures. InAP determined by properties the andinteractions oftheir Essential Knowledge 1.A.5:Systems have properties structure. collection ofobjects. Objectsare treated ashaving nointernal Essential Knowledge 1.A.1:Asystem isanobjectora Return to Table ofContents © 2017TheCollege Board Table ofContents Return to

Appendixes 113

Return to at the at → Table of Contents Table © 2017 The College Board Return to Table of Contents Table to Return Appendix A: The Big Ideas in AP Physics 1 in AP Physics Big Ideas The A:Appendix An observer in a particular 3.A.1: An observer Essential Knowledge can describe the using motion of an object frame reference velocity, such quantities as position, displacement, distance, speed, and acceleration. vectors. described by are 3.A.2: Forces Essential Knowledge on an object exerted 3.A.3: A force Essential Knowledge that of object with another due to the interaction is always object. on a force 3.A.4: If one object exerts Essential Knowledge of a force exerts a second object, the second object always direction. in object equal magnitude on thethe opposite first A vector field gives, as a gives, field 2.A.1: A vector Essential Knowledge of a perhaps time), thefunction of position (and value a vector. quantity that is described by physical g field A gravitational 2.B.1: Essential Knowledge causes a gravitational force force of an object with mass m causes a gravitational location on thethe object in direction of magnitude mg to be exerted of the field. caused field The gravitational 2.B.2: Essential Knowledge and, symmetric object with mass is radial a spherically by of the radial square as the inverse outside the object, varies of that object. the center distance from If an object of interest interacts interacts If an object of interest 3.B.1: Essential Knowledge sum of is the vector the other net force objects, with several forces. the individual useful are diagrams Free-body 3.B.2: Essential Knowledge object on a single being exerted visualizing forces tools for situation. a physical and writing the that represent equations in can result forces Restoring 3.B.3: Essential Knowledge on is exerted force motion. When a linear restoring oscillatory equilibrium position, the an object an object displaced from harmonic simple a special type of motion called will undergo the by exerted force include gravitational motion. Examples Earth pendulum and mass-spring oscillator. on a simple AP Physics 1: Algebra-Based AP Physics

. nteractions an of object with other objects can lds existing in space can be used to explain The i be described by forces. Fie interactions.

Course and Exam Description and Exam Course 3.B: Enduring Understanding of an object the acceleration Classically, with other objects can be interacting using by predicted Enduring Understanding 3.A: Enduring Understanding certain common share All forces by when considered characteristics frames. in inertial reference observers Big Idea 3: Big A field 2.A: A field Enduring Understanding of some physical a value associates point in space. quantity with every describing for useful models are Field a distance that at occur interactions as a variety as well forces) (long-range phenomena. of other physical A 2.B: Enduring Understanding by an object is caused field gravitational with mass. Big Idea 2:Big 113 114 Appendixes Appendix A: Appendix A: The BigIdeasinAPPhysics 1 fundamental. typesofforcesCertain are considered Enduring Understanding 3.G: object. on that exerted onanobjectcancauseatorque Enduring Understanding 3.F:Aforce kinetic energy object. ofthe exerted onanobjectcanchange the Enduring Understanding 3.E:Aforce object. momentum ofthe exerted onanobjectcanchange the Enduring Understanding 3.D:Aforce at-a-distance) forces orcontactforces. categorized long-range aseither (action- macroscopicthe level, forces canbe Enduring Understanding 3.C: At AP Physics 1:Algebra-Based system,on the where system isrelated netforce tothe exerted acceleration center ofthe ofmassa Enduring Understanding 4.A:The Big 4: Idea

in those systems. systems. those in Int eractions between systems can result in changes changes in result can systems between eractions .

Course andExam Description of that system.of that system, there willbenochange center-of-mass inthe velocity systems. interacting Ifthe objects are same ofthe parts areeach other duetointeractions between objectsinthe Essential Knowledge 4.A.3:Forces systems that exert on rate ofchange time. ofpositionwith of change ofvelocity time,andvelocity with isequaltothe Essential Knowledge 4.A.2:Acceleration rate isequal tothe acceleration ofitscenter ofmass. system canbedescribedby displacement,velocity, the and Essential Knowledge 4.A.1:Thelinearmotionofa scales. at allscales anddominate largest at the distanceandmass Essential Knowledge 3.G.1: Gravitational forces are exerted can change angularmomentumofanobject. the Essential Knowledge 3.F.3: Atorqueexerted onanobject axis.about that rotational motionoranobjecttochange itsrotational motion along any axiswillcausearigidsystem tochange its Essential Knowledge 3.F.2: Thepresence ofanettorque axis.that force pointofapplication ofthe the results inatorqueabout axisofrotation lineconnectingthe perpendicular tothe and Essential Knowledge 3.F.1: Only force the component forcethe isexerted. timeinterval objectduringthe displacementofthe on the that forceof anobjectdependsonthe exerted objectand onthe Essential Knowledge 3.E.1:Thechange kineticenergy inthe object occurs over atimeinterval. Essential Knowledge 3.D.2: Thechange inmomentumofan object. the object isavector direction inthe netforce ofthe exerted on Essential Knowledge 3.D.1: Thechange inmomentumofan (Physics 2). tension, friction,normal,spring(Physics 1),andbuoyant arise from interatomic electric forces. Theseforces include interaction object,andthey ofoneobjecttouchinganother Essential Knowledge 3.C.4: Contactforces result from the hasanelectric objectthat charge.another theinteraction hasanelectric ofoneobjectthat charge with Essential Knowledge 3.C.2: Electric force results from hasmass.that interaction object another hasmasswith ofoneobjectthat Essential Knowledge 3.C.1: Gravitational force describesthe

Appendixes 115

A system is an object or a 5.A.1: A system Essential Knowledge no as having treated The objects are of objects. collection structure. internal under all all systems 5.A.2: For Essential Knowledge linear momentum, and charge, energy, circumstances, or a isolated an For conserved. angular momentum are constant. An open quantities are conserved system, closed quantity with its conserved any is one that exchanges system surroundings. can be either a 5.A.3: An interaction Essential Knowledge of or the transfer objects outside the system by exerted force some quantity with objects outside the system. a 5.A.4: The boundary between Essential Knowledge the person is a decision made by and its environment system to simplify or otherwise considering the in order situation assist in analysis. The change in linear momentum in The change 4.B.1: Essential Knowledge of the mass of theis the product system a constant-mass for of mass. the of center in velocity and the change system in linear momentum The change 4.B.2: Essential Knowledge on that force of the average the product by is given of the system is exerted. during which the force the and time interval system includes of a system The energy 4.C.1: Essential Knowledge internal and microscopic energy, potential its kinetic energy, energy, potential include gravitational Examples energy. and kinetic energy. energy, elastic potential (the sum Mechanical energy 4.C.2: Essential Knowledge into or out of a is transferred energy) of kinetic and potential such that on a system is exerted force an external when system to its displacement. The is parallel a component of the force work. is called is transferred which the energy through process angular velocity, Torque, 4.D.1: Essential Knowledge and vectors and angular momentum are angular acceleration, depending upon or negative as positive can be characterized to counterclockwise rise to or correspond whether they give to an axis. with respect rotation or clockwise The angular momentum of a 4.D.2: Essential Knowledge with other objects or due to interactions change may system systems. in angular The change 4.D.3: Essential Knowledge torque and the of average the product by momentum is given during which the torque is exerted. the time interval AP Physics 1: Algebra-Based AP Physics

nges that occur as a result interactions of are Cha constrained by conservation laws.

Course and Exam Description and Exam Course Big Idea 5: Big 5.A: Certain Enduring Understanding in the sense conserved, quantities are that of those the quantities in changes equal to the always are system a given the of that quantity to or from transfer with interactions all possible by system other systems. 4.C: Enduring Understanding with other objects or Interactions of the total energy change can systems a system. 4.D: A net Enduring Understanding other by on a system torque exerted the will change objects or systems angular momentum of the system. 4.B: Enduring Understanding with other or objects Interactions the total linear can change systems momentum of a system. 115 116 Appendixes Appendix A: Appendix A: The BigIdeasinAPPhysics 1 electric charge ofasystem isconserved. Enduring Understanding 5.C: The energy ofasystem isconserved. Enduring Understanding 5.B: The AP Physics 1:Algebra-Based

Course andExam Description and along timeafter circuit the isclosed.] should belimited toopencircuit, just after circuit isclosed, steady-state situations. For circuits capacitors, with situations branch, onebattery only. Physics 2:includescapacitors in circuits resistors with in series, at mostoneparallel with combine resistors inseriesandparallel. [Physics 1:covers at eachjunctioncircuit. inthe Examples include circuits that circuits. Sincecharge isconserved, current mustbeconserved conservationdescribes the ofelectric charge inelectrical Essential Knowledge 5.C.3: Kirchhoff’s junction rule circuits, capacitors.] with includingthose developedfurther inPhysics context 2inthe ofmore complex of Kirchhoff’s laws tocircuits isintroduced inPhysics 1and conservation ofenergy inelectrical circuits. [Theapplication Essential Knowledge 5.B.9: Kirchhoff’s loop rule describes ofthermodynamics.]as apart gaswith getting compressed orexpandedistreated inPhysics 2 energy transfer into, asystem. outof,orwithin [Apistonfilled may occur at different rates. Power the isdefinedas rateof called work. Energy transfer inmechanicalorelectrical systems object orsystem through energy adistance; this transfer is external force exerted onanobjectorsystem moves that the Essential Knowledge 5.B.5: Energy canbetransferred by an makeobjects that system. upthe system potential andthe energy configuration ofthe the of kineticenergy make objectsthat includes the ofthe upthe Essential Knowledge 5.B.4: Theinternal energy ofasystem conservative forces. a system system that objectswithin ifthe interact with can have potential energy. Potential energy existswithin Essential Knowledge 5.B.3: Asystem internal with structure configuration.] examining changes ininternal energy changes with in Physics 2:includescharged objectinelectric fields and includes mass-springoscillators andsimple pendulums. structure canresult inchanges ininternal energy. [Physics 1: can have internal energy, andchanges inasystem’s internal Essential Knowledge 5.B.2: Asystem internal with structure interaction between two ormore objects. only have kineticenergy sincepotential energy requires an Essential Knowledge 5.B.1: Classically, anobjectcan

Appendixes 117

Return to Table of Contents Table © 2017 The College Board Return to Table of Contents Table to Return Appendix A: The Big Ideas in AP Physics 1 in AP Physics Big Ideas The A:Appendix A vector field gives, as a gives, field 6.A.1: A vector Essential Knowledge of a function of position (and perhaps time), the value a vector. quantity that is described by physical mechanical propagation, 6.A.2: For Essential Knowledge do not waves electromagnetic a medium, while require waves include light traveling medium. Examples a physical require a vacuum. through and sound not traveling a vacuum through 6.A.3: The amplitude is the maximum Essential Knowledge its equilibrium value. from displacement of a wave carried by the energy 6.A.4: Classically, Essential Knowledge with amplitude. Examples depends upon and increases a wave include sound waves. In a collision between objects, objects, between In a collision 5.D.1: Essential Knowledge kinetic In an elastic collision, is conserved. linear momentum and after. the is same before energy objects, In a collision between 5.D.2: Essential Knowledge inelastic collision, In an linear momentum is conserved. the collision. and after the is not same before kinetic energy of of the center The velocity 5.D.3: Essential Knowledge an interaction by cannot be changed mass of thesystem of 1: includes no calculations [Physics within the system. until Physics of mass; the is not provided equation centers 1 students Physics without doing calculations, 2. However, of mass of highly the center to locate able to be expected are or cube rod such as a uniform symmetric mass distributions, of equal mass.] spheres or two density, of uniform torque exerted 5.E.1: If the net external Essential Knowledge the momentum of the angular system is zero, on the system does not change. 5.E.2: The angular momentum of Essential Knowledge of and velocities the locations by is determined a system inertia The rotational up thethe system. objects thatmake depends upon the distribution of of an object or system of in the radius Changes mass within the object or system. or in the distribution of mass within thea system system inertia, and hence rotational in the system’s in changes result angular a given for and linear speed in its angular velocity orbits in an Earth- include elliptical momentum. Examples the moments of for expressions Mathematical system. satellite needed. Students will not be where be provided inertia should axis theorem. the to know parallel expected AP Physics 1: Algebra-Based AP Physics

s can transfer energy and momentum from one Wave location to another without the permanent transfer massof and serve as a mathematical the model for description of other phenomena.

Course and Exam Description and Exam Course Enduring Understanding 6.A: A wave Enduring Understanding disturbance that transfers is a traveling and momentum. energy Big Idea 6:Big Enduring Understanding 5.E: The Enduring Understanding is angular momentum of a system conserved. Enduring Understanding 5.D: The Enduring Understanding is of a system linear momentum conserved. 117 118 Appendixes Appendix A: Appendix A: The BigIdeasinAPPhysics 1 standing waves andbeats. Interference andsuperpositionlead to Enduring Understanding 6.D: energy. frequency, wavelength, speed,and and canbedescribedby itsamplitude, timeandposition a functionofboth periodic wave repeats isonethat as Enduring Understanding 6.B: A AP Physics 1:Algebra-Based

Course andExam Description waves ofslightly different frequency. Essential Knowledge 6.D.5: Beats arisefrom addition of the which itisconfined. a standingwave are determined region by size ofthe the to Essential Knowledge 6.D.4: Thepossible wavelengths of closed andopentubes. waves onafixed ofstringandsound length waves inboth to aregion andhave nodesandantinodes. Examples include additionofincidentandreflectedthe wavesthat are confined Essential Knowledge 6.D.3: Standingwaves are result the of resultantin the wave. can interact insuchaway astoproduce amplitudevariations Essential Knowledge 6.D.2: Two ormore traveling waves This iscalled superposition. determined two by pulses. displacements ofthe addingthe Where pulsesoverlap, the resulting the displacementcanbe donotbounceoffeachother.through they eachother; resultantin the wave. Whentwo pulsescross, travel they interact insuchaway as toproduce amplitudevariations Essential Knowledge 6.D.1: Two ormore wave pulsescan This isaqualitative treatment only. wave relative dependsonthe motionofsource andobserver. Essential Knowledge 6.B.5: Theobserved frequency ofa ratiois the ofspeedover frequency. Essential Knowledge 6.B.4: For aperiodicwave, wavelength wavelength repeat isthe wave. distanceofthe Essential Knowledge 6.B.2: For aperiodicwave, the repetitions wave ofthe perunittime. repeatis the wave. timeofthe Thefrequency number isthe of Essential Knowledge 6.B.1: For aperiodicwave, period the

Appendixes 119

Return to Table of Contents Table © 2017 The College Board Return to Table of Contents Table to Return Big Ideas 3 1, 2, 3, 4 1, 2, 3, 4 3, 5 3, 4, 5 3, 4, 5 3, 4, 5 1, 3, 5 1, 5 6 AP Physics 1: Algebra-Based AP Physics

Appendix B: Developing Big Ideas from Foundational Physics Principles Physics Foundational from Big Ideas B: Developing Appendix

Course and Exam Description and Exam Course Kinematics (1D and 2D) Kinematics The table below helps illustrate how to make connections across the course framework framework the course connections across to make how helps illustrate below The table 1 Principles Physics by developing big ideas from the foundational physics principles. physics the foundational big ideas from developing by Laws Dynamics: Newton’s of Gravitation Law Motion and Universal Circular and Pendulum Simple Harmonic Motion: Simple Mass-Spring Systems of Impulse, Linear Momentum, and Conservation Linear Momentum: Collisions of Energy and Conservation Energy, Work, and Kinematics Rotational Motion: Torque, Rotational of and Conservation Dynamics, Rotational Energy, Angular Momentum Force and Electric Charge Electric Electrostatics: Only Resistors DC Circuits: and Sound Mechanical Waves Appendix B: Developing Appendix B: Developing FoundationalBig Ideas from Principles Physics 119 120 Appendixes classes inorder content. their tobecomefamiliar with exam tables room, tothe of these may they although throughout year usethem the intheir takewhen they APPhysics the 1Exam. Therefore, studentsmay NOT own copies bringtheir The accompanying table ofinformation andequation tables willbeprovided tostudents Table ofInformation andEquation Tables for APPhysics the 1Exam Constants and Equations Physics C: AP 1 Appendix AP Physics 1:Algebra-Based conventions, butinsomecasesconsistency was sacrificed the sakefor ofclarity. for symbolsusedinwritingequations. the Theequation tables follow many common in different tables. Itshould benotedtherethat isnouniform convention among textbooks defined. However,the samesymbolisusedto insomecases represent different quantities appear.they Within symbolsusedfor variables eachsection,the the sectionare inthat The equation tables are grouped insectionsaccording majorcontent tothe category inwhich equation isapplicable. physical principles underlieeachequation that andfor conditionsfor knowing the whicheach special casesofany are that tables. inthe Studentsare responsible for understanding the tables.by equations inthe combiningother Nor include equations are dothey that simply might possibly beused.For example, donotincludemany they equations canbederived that APPhysicsin the 1course andexam. However, tables donotincludeallequations the that tablesThe equations express inthe relationships the are that encountered mostfrequently exams exceptboth for conventions. someofthe free-responsemultiple-choice sectionandthe section. The table ofinformation equation tables andthe are printed front nearthe cover of tables (apcentral.collegeboard.org). PhysicsCheck the course homepages onAPCentral for latest the versions ofthese tables.of the That date willonly bechanged whenthere isarevision toany tables. ofthe Some explanations equation aboutnotation tables: usedinthe 5. 4. 3. 2. 1.

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Course andExam Description ariable inan equation specifically indicates achange in sical constants are the same as those in the Tablesical constantsare inthe sameasthose the of d, r, s,h,l ) are usedfor lineardimensionssuchas T The headings list the effectiveThe headingslistthe date e usedtorepresent specialcasesofthe he table of i nformation isidenticalfor Return to Table ofContents © 2017TheCollege Board Table ofContents the the both Return to

Appendixes 121

AP Physics 1: Algebra-Based AP Physics

Course and Exam Description and Exam Course Appendix C: AP Physics 1 Equations and Constants and 1 Equations Physics C: AP Appendix 121 122 Appendixes Appendix C:APPhysics 1Equations andConstants AP Physics 1: Algebra-Based

Course and Exam Description

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