DOCSLIB.ORG

Weight, Mass, and Gravity: Threshold Concepts in Learning Science

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Weight, Mass, and Gravity: Threshold Concepts in Learning Science Varda Bar, Yaffa Brosh, and Cary Sneider Weight, Mass, and Gravity: Threshold Concepts in Learning Science Abstract information to fi x some of the most glar- a bright seventh grader is interviewed Threshold concepts are essential ideas ing problems. A recent step in the right before and after a class on photosynthe- about the natural world that present ei- direction has been development of Next sis. Prior to the class he is asked what a ther a barrier or a gateway to a deep un- Generation Science Standards (NGSS tree is mostly made from. His response derstanding of science. Weight, mass, Lead States, 2013) in the United States, is that it is made from soil and water. and gravity are threshold concepts that but it is just that—a step. The new stan- After a six-day unit on photosynthe- underpin students’ abilities to understand dards provide clear targets for assess- sis, during which he experienced a lab important ideas in all fi elds of science, ment, but do not provide a pathway for activity coordinated with lectures on embodied in the performance expecta- reaching them. how plants extract carbon from carbon tions in the Next Generation Science In this paper, we argue that to meet dioxide in the air, and learns about the Standards (NGSS). This study begins the new standards curriculum develop- chemistry of photosynthesis, he was with a review of research on students’ ers and teachers must focus on help- again asked the same question. Despite diffi culties in understanding these con- ing students develop deep, fl exible, and instruction from a knowledgeable teacher, cepts individually and in relation to each useful threshold concepts that provide he again gives the same answer—that the other, based on individual interviews and the intellectual underpinnings of the material in a tree comes from soil and surveys of several hundred children that standards. To illustrate this instructional water. Although he correctly stated the illustrate how students’ understanding strategy we have chosen the concepts chemical equation for photosynthesis, of weight, mass, and gravity develops of weight, mass, and gravity, since they when asked if the wood, bark, and leaves over the lifespan, from age fi ve through are essential for grasping a number of come mostly from carbon dioxide in the adult. New data from an additional 451 performance expectations in all dis- air, he replies that is impossible because subjects in the critical age range of 10 ciplinary areas. While we understand air doesn’t weigh anything, stating “If to 14 years old support and extend the and support the new vision for three- it did we wouldn’t be able to breathe.” prior fi ndings. The purpose of the cur- dimensional instruction (i.e., combin- Although it may not be surprising that rent study is to provide teachers and ing practices, crosscutting concepts, seventh grade students have diffi culty curriculum developers with actionable and core ideas) implicit in the NGSS, understanding that gases have weight, and up-to-date information that educa- we claim that the need to help children the same video shows that graduates tors can use to help children at the up- grasp fundamental concepts continues from Harvard and MIT give the same per elementary, middle, and high school to be important. answer as the high school student—that levels achieve Next Generation Science The diffi culties posed by students’ in- the considerable mass of a tree could not Standards. ability to understand and differentiate the possibly have come from carbon in the concepts of weight and mass are well air. Like the seventh grader, the college Introduction known in physics. Klopfer, Champagne, graduates had no diffi culty memorizing Large parts of our nations’ science and Chaiklin (1992) noted that children the chemical formula for photosynthe- education systems are broken, and we enter school with initial ideas about sis, but when they really thought about have known about some of the problems certain essential “ubiquitous quanti- it, even that classic example of conserva- through educational research for de- ties” (e.g., weight, mass, volume and tion of mass seemed like they were get- cades (U.S. National Commission on density), and that a goal of science in- ting something (wood, bark, and leaves) Excellence in Education, 1983; Fleishman, struction is to develop the spontaneous from nothing (the air.) 2010; Martin et. al, 2012). It’s time concepts into a scientifi c understand- The third threshold concept that we to bring these fi ndings to a broader au- ing of these quantities—a goal that will describe in this paper is the mean- dience so that practitioners can use the the authors acknowledged was only ing of gravity, which also seems to be rarely achieved, even by the time stu- poorly learned at the middle school level Keywords: middle school, standards, physical dents reach college. (Kavanagh and Sneider, 2007a, 2007b), science, weight, mass, gravity In a compelling video, entitled “Lessons with misconceptions continuing into adult- from Thin Air” (Schneps & Sadler, 1997), hood. Recognizing that understanding 22 SCIENCE EDUCATOR of basic physics concepts are important climate and the interaction of Earth falling, or being thrown upwards. This is for the study of geology, college profes- systems. also an area that has been widely stud- sors Ashghar and Libarkin (2010) sur- 5-PS1-2. Measure and graph quan- ied, but for which some questions still veyed 197 students enrolled in geology tities to provide evidence that re- remain (Agan & Sneider, 2004). courses at a mid-western university con- gardless of the type of change that The present investigation has been cerning their understanding of gravity. occurs when heating, cooling, or undertaken to provide a fi ner-grained anal- They found that only 21% had the cor- mixing substances, the total weight ysis of students’ schemas during the crit- rect scientifi c idea that gravity is a force of matter is conserved. ical period ages 10 to 14, when students of attraction, and that very few students are expected to develop an initial scien- incorporated the concepts of attraction, The concept underpinning this perfor- tifi c understanding of gravity, weight, mass, and force into their explanations mance expectation is conservation of and mass and their interconnections. of gravity. Various students expressed weight under phase transformations, Although there is an extensive litera- the ideas that Earth’s “spin,” “magnetism,” which can be very challenging for fi fth ture on students’ understanding of these and “atmosphere” caused the force of grade students (Galili & Bar, 1997), as threshold concepts, most of the studies attraction between Earth and other ob- we will discuss in our literature review. were done decades ago, so the fi ndings jects. The researchers identifi ed gravity MS-PS2-2. Plan an investigation to may not be true of today’s students. By as one of a small group of important provide evidence that the change in conducting a systematic study of chil- threshold concepts that can act as bar- an object’s motion depends on the dren’s ideas across a broad age range riers to learning, or provide a gateway sum of the forces on the object and we hope to provide teachers and curricu- to deep understanding of many related the mass of the object. lum developers with the actionable and concepts. Concepts underlying this performance up-to-date information that they need to In this paper, we have chosen to focus expectation include mass, as embodied help students at the upper elementary, on weight, mass and gravity since these in Newton’s Laws of Motion, and also middle, and high school levels achieve terms are interrelated threshold concepts the relationship between force and mo- Next Generation Science Standards. for several of the performance expecta- tion which is subject to the common tions in the Next Generation Science misconception that gravity does not act Historical Background Standards (NGSS Lead States, 2013). on all objects, however they may be mov- In many cases the trajectory of a As the NGSS becomes widely adopted, ing. For example, many students believe child’s understanding of a concept may students will be expected to have a ro- that gravity does not act on an object that parallel the development of a concept in bust scientifi c understanding of these has been thrown upward, until it reverses the history of science. Consequently, a concepts in order to achieve a number direction and starts to fall (Palmer, 2001). brief historical review can provide use- of performance expectations. Following ful insights for researchers by suggesting is a list of performance expectations that MS - ESS2 - 4. Develop a model the possible causes of learners’ diffi cul- require understanding of weight, mass, to describe the cycling of water ties, as well as for teachers to be aware and/or gravity. through Earth’s systems driven by of possible misconceptions that their 1 energy from the sun and the force of students may hold. Children can also 5-LS1-1. Support an argument that gravity. plants get the materials they need benefi t from accounts of scientists of the for growth chiefl y from air and Traditionally the water cycle has been distant past who may have shared some water. taught at the elementary level. Mov- of their own ideas about the world, and ing it to the middle school will make it how the scientists eventually changed If it were not for the compelling illustra- more accessible, but still challenging as their ideas as a result of new data, or new tion on the video, it might not be obvious it requires students to conserve matter ways of thinking (Bar and Zinn, 1998).
Load more

Recommended publications
  • The Experimental Determination of the Moment of Inertia of a Model Airplane Michael Koken [email protected]
    The University of Akron IdeaExchange@UAkron The Dr. Gary B. and Pamela S. Williams Honors Honors Research Projects College Fall 2017 The Experimental Determination of the Moment of Inertia of a Model Airplane Michael Koken [email protected] Please take a moment to share how this work helps you through this survey. Your feedback will be important as we plan further development of our repository. Follow this and additional works at: http://ideaexchange.uakron.edu/honors_research_projects Part of the Aerospace Engineering Commons, Aviation Commons, Civil and Environmental Engineering Commons, Mechanical Engineering Commons, and the Physics Commons Recommended Citation Koken, Michael, "The Experimental Determination of the Moment of Inertia of a Model Airplane" (2017). Honors Research Projects. 585. http://ideaexchange.uakron.edu/honors_research_projects/585 This Honors Research Project is brought to you for free and open access by The Dr. Gary B. and Pamela S. Williams Honors College at IdeaExchange@UAkron, the institutional repository of The nivU ersity of Akron in Akron, Ohio, USA. It has been accepted for inclusion in Honors Research Projects by an authorized administrator of IdeaExchange@UAkron. For more information, please contact [email protected], [email protected]. 2017 THE EXPERIMENTAL DETERMINATION OF A MODEL AIRPLANE KOKEN, MICHAEL THE UNIVERSITY OF AKRON Honors Project TABLE OF CONTENTS List of Tables ................................................................................................................................................
    [Show full text]
  • Kaluza-Klein Gravity, Concentrating on the General Rel- Ativity, Rather Than Particle Physics Side of the Subject
    Kaluza-Klein Gravity J. M. Overduin Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 and P. S. Wesson Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1 and Gravity Probe-B, Hansen Physics Laboratories, Stanford University, Stanford, California, U.S.A. 94305 Abstract We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identi- fied and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time. arXiv:gr-qc/9805018v1 7 May 1998 Preprint submitted to Elsevier Preprint 3 February 2008 1 Introduction Kaluza’s [1] achievement was to show that five-dimensional general relativity contains both Einstein’s four-dimensional theory of gravity and Maxwell’s the- ory of electromagnetism. He however imposed a somewhat artificial restriction (the cylinder condition) on the coordinates, essentially barring the fifth one a priori from making a direct appearance in the laws of physics. Klein’s [2] con- tribution was to make this restriction less artificial by suggesting a plausible physical basis for it in compactification of the fifth dimension. This idea was enthusiastically received by unified-field theorists, and when the time came to include the strong and weak forces by extending Kaluza’s mechanism to higher dimensions, it was assumed that these too would be compact. This line of thinking has led through eleven-dimensional supergravity theories in the 1980s to the current favorite contenders for a possible “theory of everything,” ten-dimensional superstrings.
    [Show full text]
  • Unification of Gravity and Quantum Theory Adam Daniels Old Dominion University, [email protected]
    Old Dominion University ODU Digital Commons Faculty-Sponsored Student Research Electrical & Computer Engineering 2017 Unification of Gravity and Quantum Theory Adam Daniels Old Dominion University, [email protected] Follow this and additional works at: https://digitalcommons.odu.edu/engineering_students Part of the Elementary Particles and Fields and String Theory Commons, Engineering Physics Commons, and the Quantum Physics Commons Repository Citation Daniels, Adam, "Unification of Gravity and Quantum Theory" (2017). Faculty-Sponsored Student Research. 1. https://digitalcommons.odu.edu/engineering_students/1 This Report is brought to you for free and open access by the Electrical & Computer Engineering at ODU Digital Commons. It has been accepted for inclusion in Faculty-Sponsored Student Research by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. Unification of Gravity and Quantum Theory Adam D. Daniels [email protected] Electrical and Computer Engineering Department, Old Dominion University Norfolk, Virginia, United States Abstract- An overview of the four fundamental forces of objects falling on earth. Newton’s insight was that the force that physics as described by the Standard Model (SM) and prevalent governs matter here on Earth was the same force governing the unifying theories beyond it is provided. Background knowledge matter in space. Another critical step forward in unification was of the particles governing the fundamental forces is provided, accomplished in the 1860s when James C. Maxwell wrote down as it will be useful in understanding the way in which the his famous Maxwell’s Equations, showing that electricity and unification efforts of particle physics has evolved, either from magnetism were just two facets of a more fundamental the SM, or apart from it.
    [Show full text]
  • Post-Newtonian Approximation
    Post-Newtonian gravity and gravitational-wave astronomy Polarization waveforms in the SSB reference frame Relativistic binary systems Effective one-body formalism Post-Newtonian Approximation Piotr Jaranowski Faculty of Physcis, University of Bia lystok,Poland 01.07.2013 P. Jaranowski School of Gravitational Waves, 01{05.07.2013, Warsaw Post-Newtonian gravity and gravitational-wave astronomy Polarization waveforms in the SSB reference frame Relativistic binary systems Effective one-body formalism 1 Post-Newtonian gravity and gravitational-wave astronomy 2 Polarization waveforms in the SSB reference frame 3 Relativistic binary systems Leading-order waveforms (Newtonian binary dynamics) Leading-order waveforms without radiation-reaction effects Leading-order waveforms with radiation-reaction effects Post-Newtonian corrections Post-Newtonian spin-dependent effects 4 Effective one-body formalism EOB-improved 3PN-accurate Hamiltonian Usage of Pad´eapproximants EOB flexibility parameters P. Jaranowski School of Gravitational Waves, 01{05.07.2013, Warsaw Post-Newtonian gravity and gravitational-wave astronomy Polarization waveforms in the SSB reference frame Relativistic binary systems Effective one-body formalism 1 Post-Newtonian gravity and gravitational-wave astronomy 2 Polarization waveforms in the SSB reference frame 3 Relativistic binary systems Leading-order waveforms (Newtonian binary dynamics) Leading-order waveforms without radiation-reaction effects Leading-order waveforms with radiation-reaction effects Post-Newtonian corrections Post-Newtonian spin-dependent effects 4 Effective one-body formalism EOB-improved 3PN-accurate Hamiltonian Usage of Pad´eapproximants EOB flexibility parameters P. Jaranowski School of Gravitational Waves, 01{05.07.2013, Warsaw Relativistic binary systems exist in nature, they comprise compact objects: neutron stars or black holes. These systems emit gravitational waves, which experimenters try to detect within the LIGO/VIRGO/GEO600 projects.
    [Show full text]
  • Multidisciplinary Design Project Engineering Dictionary Version 0.0.2
    Multidisciplinary Design Project Engineering Dictionary Version 0.0.2 February 15, 2006 . DRAFT Cambridge-MIT Institute Multidisciplinary Design Project This Dictionary/Glossary of Engineering terms has been compiled to compliment the work developed as part of the Multi-disciplinary Design Project (MDP), which is a programme to develop teaching material and kits to aid the running of mechtronics projects in Universities and Schools. The project is being carried out with support from the Cambridge-MIT Institute undergraduate teaching programe. For more information about the project please visit the MDP website at http://www-mdp.eng.cam.ac.uk or contact Dr. Peter Long Prof. Alex Slocum Cambridge University Engineering Department Massachusetts Institute of Technology Trumpington Street, 77 Massachusetts Ave. Cambridge. Cambridge MA 02139-4307 CB2 1PZ. USA e-mail: [email protected] e-mail: [email protected] tel: +44 (0) 1223 332779 tel: +1 617 253 0012 For information about the CMI initiative please see Cambridge-MIT Institute website :- http://www.cambridge-mit.org CMI CMI, University of Cambridge Massachusetts Institute of Technology 10 Miller’s Yard, 77 Massachusetts Ave. Mill Lane, Cambridge MA 02139-4307 Cambridge. CB2 1RQ. USA tel: +44 (0) 1223 327207 tel. +1 617 253 7732 fax: +44 (0) 1223 765891 fax. +1 617 258 8539 . DRAFT 2 CMI-MDP Programme 1 Introduction This dictionary/glossary has not been developed as a definative work but as a useful reference book for engi- neering students to search when looking for the meaning of a word/phrase. It has been compiled from a number of existing glossaries together with a number of local additions.
    [Show full text]
  • Summer Mass Schedule 2019 Layout 1 5/16/2019 4:18 PM Page 1
    Summer Mass Schedule 2019_Layout 1 5/16/2019 4:18 PM Page 1 MAY 23, 2014 S U M M E R M A S S S C H E D U L E CATHOLIC STAR HERALD — 9 Atlantic County: Our Lady of Sorrows, 5012 Dune Drive, Avalon Sat: 5 PM; Sun: 10 AM Wabash & Poplar Aves., Linwood Daily Mass: Mon-Fri 8:30AM (starting July Parish of St. John Neumann St. Elizabeth Ann Seton, Daily Mass: Mon-Fri 7:45 AM; Sat: 8 AM, 1), Sat: 8:30 AM; Sat: 5 PM; Sun: 7, 8:15, St. John of God Church, 591 New Jersey Ave., Absecon Tue: 6:30 PM Mass & devotion to St. 9:30, 11 AM, 12:15 PM, 5 PM; 680 Town Bank Rd., North Cape May Daily Mass: Mon-Fri: 6:45 AM; Sat: 5 PM; Anthony; Sat: 5 PM; Sun: 8 AM, 10 AM, Confessions: Following the Sat morning Daily Mass: Mon-Fri: 9 AM; Sat: 4 PM; Sun: 8 AM, 10 AM, 11:30 AM; 6:30 PM; Holy Days: 6:30 Vigil, 7:45 AM, daily Mass; & 3:45 – 4:30 PM Sat Sun: 10 AM; Holy Days: 9 AM & 7 PM on Confessions: Sat: 4 - 4:30 PM & 6 - 6:30 PM; 6:30 PM; Confessions: Sat: 3:45 PM; Sacred Heart Church, Holy Day; Confessions: Wed after 9 AM Holy Day Vigil: 7 PM; Holy Day: 6:45 AM Perpetual Adoration in church seven days 25th and First Street, Avalon Mass, Sat 2:30 – 3:30 PM; Adoration: & 9 AM a week, 24-hours a day.
    [Show full text]
  • Einstein's Gravitational Field
    Einstein’s gravitational field Abstract: There exists some confusion, as evidenced in the literature, regarding the nature the gravitational field in Einstein’s General Theory of Relativity. It is argued here that this confusion is a result of a change in interpretation of the gravitational field. Einstein identified the existence of gravity with the inertial motion of accelerating bodies (i.e. bodies in free-fall) whereas contemporary physicists identify the existence of gravity with space-time curvature (i.e. tidal forces). The interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with. 1 Author: Peter M. Brown e-mail: [email protected] 2 INTRODUCTION Einstein’s General Theory of Relativity (EGR) has been credited as the greatest intellectual achievement of the 20th Century. This accomplishment is reflected in Time Magazine’s December 31, 1999 issue 1, which declares Einstein the Person of the Century. Indeed, Einstein is often taken as the model of genius for his work in relativity. It is widely assumed that, according to Einstein’s general theory of relativity, gravitation is a curvature in space-time. There is a well- accepted definition of space-time curvature. As stated by Thorne 2 space-time curvature and tidal gravity are the same thing expressed in different languages, the former in the language of relativity, the later in the language of Newtonian gravity. However one of the main tenants of general relativity is the Principle of Equivalence: A uniform gravitational field is equivalent to a uniformly accelerating frame of reference. This implies that one can create a uniform gravitational field simply by changing one’s frame of reference from an inertial frame of reference to an accelerating frame, which is rather difficult idea to accept.
    [Show full text]
  • Principle of Relativity and Inertial Dragging
    ThePrincipleofRelativityandInertialDragging By ØyvindG.Grøn OsloUniversityCollege,Departmentofengineering,St.OlavsPl.4,0130Oslo, Norway Email: [email protected] Mach’s principle and the principle of relativity have been discussed by H. I. HartmanandC.Nissim-Sabatinthisjournal.Severalphenomenaweresaidtoviolate the principle of relativity as applied to rotating motion. These claims have recently been contested. However, in neither of these articles have the general relativistic phenomenonofinertialdraggingbeeninvoked,andnocalculationhavebeenoffered byeithersidetosubstantiatetheirclaims.HereIdiscussthepossiblevalidityofthe principleofrelativityforrotatingmotionwithinthecontextofthegeneraltheoryof relativity, and point out the significance of inertial dragging in this connection. Although my main points are of a qualitative nature, I also provide the necessary calculationstodemonstratehowthesepointscomeoutasconsequencesofthegeneral theoryofrelativity. 1 1.Introduction H. I. Hartman and C. Nissim-Sabat 1 have argued that “one cannot ascribe all pertinentobservationssolelytorelativemotionbetweenasystemandtheuniverse”. They consider an UR-scenario in which a bucket with water is atrest in a rotating universe,andaBR-scenariowherethebucketrotatesinanon-rotatinguniverseand givefiveexamplestoshowthatthesesituationsarenotphysicallyequivalent,i.e.that theprincipleofrelativityisnotvalidforrotationalmotion. When Einstein 2 presented the general theory of relativity he emphasized the importanceofthegeneralprincipleofrelativity.Inasectiontitled“TheNeedforan
    [Show full text]
  • Christmas Eve/Christmas Day Parish Mass Schedules
    Christmas Eve/Christmas Day Parish Mass Schedules Parish Christmas Eve Christmas Day Zip (Louisville unless noted) (p.m. unless noted; check local time zone) (a.m. unless noted; check local time zone) Cathedral of the Assumption 40202 5:30, Midnight 9:30, Noon Saint Agnes 40205 5:30, 8:00, 10:30 9:00, 11:30 Saint Albert the Great 40222 5:00, 8:00, Midnight 10:00 All Saints, Taylorsville 40071 4:00 9:00 Saint Aloysius, Pewee Valley 40056 4:30, 8:00 11:00 Saint Aloysius, Shepherdsville 40165 4:00 9:30 Saint Ambrose, Cecilia 42724 — 10:00 Saint Ann, Howardstown 40051 8:00 10:00 Annunciation, Shelbyville 40065 5:30, 7:30 (Spanish), 11:00 9:00 Ascension 40220 5:30, 10:00 10:30 Saint Athanasius 40219 5:00, 11:00 10:00 Saint Augustine, Lebanon 40033 4:00, 6:30, 9:00 9:00 Saint Augustine 40203 10:00 (Carols at 9:30) — Saint Barnabas 40220 4:30, 9:00 10:00 Saint Bartholomew 40218 4:00 (English), 8:00 (Spanish), 11:00 (English) 10:00 (English) Saint Benedict, Lebanon Junction 40150 6:00 — Saint Bernadette 40059 6:00, 9:00 9:00 Saint Bernard, Clementsville 42539 Midnight 9:00 Saint Bernard 40228 7:00, 11:00 9:00 Saint Boniface 40202 5:00 (Highland Players at 4:00) 11:00 Saint Brigid 40204 5:00 8:00, 10:15 Saint Brigid, Vine Grove 40175 4:00, 9:00 10:00 Saint Catherine, New Haven 40051 4:00 9:00 Saint Charles, St. Mary 40033 4:00 10:45 Christ the Healer, Edmonton 42129 6:00 (Central Time) 11:00 (Central Time) Christ the King 40211 9:00 p.m.
    [Show full text]
  • 5D Kaluza-Klein Theories - a Brief Review
    5D Kaluza-Klein theories - a brief review Andr´eMorgado Patr´ıcio, no 67898 Departamento de F´ısica, Instituto Superior T´ecnico, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal (Dated: 21 de Novembro de 2013) We review Kaluza-Klein theory in five dimensions from the General Relativity side. Kaluza's original idea is examined and two distinct approaches to the subject are presented and contrasted: compactified and noncompactified theories. We also discuss some cosmological implications of the noncompactified theory at the end of this paper. ^ ^ 1 ^ I. INTRODUCTION where GAB ≡ RAB − 2 g^ABR is the Einstein tensor. Inspired by the ties between Minkowki's 4D space- For the metric, we identify the αβ-part ofg ^AB with time and Maxwell's EM unification, Nordstr¨om[3] in 1914 gαβ, the α4-part as the electromagnetic potential Aα and and Kaluza[4] in 1921 showed that 5D general relativ- g^44 with a scalar field φ, parametrizing it as follows: ity contains both Einstein's 4D gravity and Maxwell's g + κ2φ2A A κφ2A EM. However, they imposed an artificial restriction of no g^ (x; y) = αβ α β α ; (4) AB κφ2A φ2 dependence on the fifth coordinate (cylinder condition). β Klein[5], in 1926, suggested a physical basis to avoid this where κ is a multiplicative factor. If we identifyp it in problem in the compactification of the fifth dimension, terms of the 4D gravitational constant by κ = 4 πG, idea now used in higher-dimensional generalisations to then, using the metric4 and applying the cylinder con- include weak and strong interactions.
    [Show full text]
  • Center of Mass Moment of Inertia
    Lecture 19 Physics I Chapter 12 Center of Mass Moment of Inertia Course website: http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsI PHYS.1410 Lecture 19 Danylov Department of Physics and Applied Physics IN THIS CHAPTER, you will start discussing rotational dynamics Today we are going to discuss: Chapter 12: Rotation about the Center of Mass: Section 12.2 (skip “Finding the CM by Integration) Rotational Kinetic Energy: Section 12.3 Moment of Inertia: Section 12.4 PHYS.1410 Lecture 19 Danylov Department of Physics and Applied Physics Center of Mass (CM) PHYS.1410 Lecture 19 Danylov Department of Physics and Applied Physics Center of Mass (CM) idea We know how to address these problems: How to describe motions like these? It is a rigid object. Translational plus rotational motion We also know how to address this motion of a single particle - kinematic equations The general motion of an object can be considered as the sum of translational motion of a certain point, plus rotational motion about that point. That point is called the center of mass point. PHYS.1410 Lecture 19 Danylov Department of Physics and Applied Physics Center of Mass: Definition m1r1 m2r2 m3r3 Position vector of the CM: r M m1 m2 m3 CM total mass of the system m1 m2 m3 n 1 The center of mass is the rCM miri mass-weighted center of M i1 the object Component form: m2 1 n m1 xCM mi xi r2 M i1 rCM (xCM , yCM , zCM ) n r1 1 yCM mi yi M i1 r 1 n 3 m3 zCM mi zi M i1 PHYS.1410 Lecture 19 Danylov Department of Physics and Applied Physics Example Center
    [Show full text]
  • Newton Euler Equations of Motion Examples
    Newton Euler Equations Of Motion Examples Alto and onymous Antonino often interloping some obligations excursively or outstrikes sunward. Pasteboard and Sarmatia Kincaid never flits his redwood! Potatory and larboard Leighton never roller-skating otherwhile when Trip notarizes his counterproofs. Velocity thus resulting in the tumbling motion of rigid bodies. Equations of motion Euler-Lagrange Newton-Euler Equations of motion. Motion of examples of experiments that a random walker uses cookies. Forces by each other two examples of example are second kind, we will refer to specify any parameter in. 213 Translational and Rotational Equations of Motion. Robotics Lecture Dynamics. Independence from a thorough description and angular velocity as expected or tofollowa userdefined behaviour does it only be loaded geometry in an appropriate cuts in. An interface to derive a particular instance: divide and author provides a positive moment is to express to output side can be run at all previous step. The analysis of rotational motions which make necessary to decide whether rotations are. For xddot and whatnot in which a very much easier in which together or arena where to use them in two backwards operation complies with respect to rotations. Which influence of examples are true, is due to independent coordinates. On sameor adjacent joints at each moment equation is also be more specific white ellipses represent rotations are unconditionally stable, for motion break down direction. Unit quaternions or Euler parameters are known to be well suited for the. The angular momentum and time and runnable python code. The example will be run physics examples are models can be symbolic generator runs faster rotation kinetic energy.
    [Show full text]