Week 11: Chapter 11
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Rotational Motion (The Dynamics of a Rigid Body)
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body) Henry Semat City College of New York Robert Katz University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/physicskatz Part of the Physics Commons Semat, Henry and Katz, Robert, "Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body)" (1958). Robert Katz Publications. 141. https://digitalcommons.unl.edu/physicskatz/141 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Robert Katz Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 11 Rotational Motion (The Dynamics of a Rigid Body) 11-1 Motion about a Fixed Axis The motion of the flywheel of an engine and of a pulley on its axle are examples of an important type of motion of a rigid body, that of the motion of rotation about a fixed axis. Consider the motion of a uniform disk rotat ing about a fixed axis passing through its center of gravity C perpendicular to the face of the disk, as shown in Figure 11-1. The motion of this disk may be de scribed in terms of the motions of each of its individual particles, but a better way to describe the motion is in terms of the angle through which the disk rotates. -
Outline of Physical Science
Outline of physical science “Physical Science” redirects here. It is not to be confused • Astronomy – study of celestial objects (such as stars, with Physics. galaxies, planets, moons, asteroids, comets and neb- ulae), the physics, chemistry, and evolution of such Physical science is a branch of natural science that stud- objects, and phenomena that originate outside the atmosphere of Earth, including supernovae explo- ies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a “physical sions, gamma ray bursts, and cosmic microwave background radiation. science”, together called the “physical sciences”. How- ever, the term “physical” creates an unintended, some- • Branches of astronomy what arbitrary distinction, since many branches of physi- cal science also study biological phenomena and branches • Chemistry – studies the composition, structure, of chemistry such as organic chemistry. properties and change of matter.[8][9] In this realm, chemistry deals with such topics as the properties of individual atoms, the manner in which atoms form 1 What is physical science? chemical bonds in the formation of compounds, the interactions of substances through intermolecular forces to give matter its general properties, and the Physical science can be described as all of the following: interactions between substances through chemical reactions to form different substances. • A branch of science (a systematic enterprise that builds and organizes knowledge in the form of • Branches of chemistry testable explanations and predictions about the • universe).[1][2][3] Earth science – all-embracing term referring to the fields of science dealing with planet Earth. Earth • A branch of natural science – natural science science is the study of how the natural environ- is a major branch of science that tries to ex- ment (ecosphere or Earth system) works and how it plain and predict nature’s phenomena, based evolved to its current state. -
Rotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn that where the force is applied and how the force is applied is just as important as how much force is applied when we want to make something rotate. This tutorial discusses the dynamics of an object rotating about a fixed axis and introduces the concepts of torque and moment of inertia. These concepts allows us to get a better understanding of why pushing a door towards its hinges is not very a very effective way to make it open, why using a longer wrench makes it easier to loosen a tight bolt, etc. This module begins by looking at the kinetic energy of rotation and by defining a quantity known as the moment of inertia which is the rotational analog of mass. Then it proceeds to discuss the quantity called torque which is the rotational analog of force and is the physical quantity that is required to changed an object's state of rotational motion. Moment of Inertia Kinetic Energy of Rotation Consider a rigid object rotating about a fixed axis at a certain angular velocity. Since every particle in the object is moving, every particle has kinetic energy. To find the total kinetic energy related to the rotation of the body, the sum of the kinetic energy of every particle due to the rotational motion is taken. The total kinetic energy can be expressed as .. -
Thermodynamic Processes: the Limits of Possible
Thermodynamic Processes: The Limits of Possible Thermodynamics put severe restrictions on what processes involving a change of the thermodynamic state of a system (U,V,N,…) are possible. In a quasi-static process system moves from one equilibrium state to another via a series of other equilibrium states . All quasi-static processes fall into two main classes: reversible and irreversible processes . Processes with decreasing total entropy of a thermodynamic system and its environment are prohibited by Postulate II Notes Graphic representation of a single thermodynamic system Phase space of extensive coordinates The fundamental relation S(1) =S(U (1) , X (1) ) of a thermodynamic system defines a hypersurface in the coordinate space S(1) S(1) U(1) U(1) X(1) X(1) S(1) – entropy of system 1 (1) (1) (1) (1) (1) U – energy of system 1 X = V , N 1 , …N m – coordinates of system 1 Notes Graphic representation of a composite thermodynamic system Phase space of extensive coordinates The fundamental relation of a composite thermodynamic system S = S (1) (U (1 ), X (1) ) + S (2) (U-U(1) ,X (2) ) (system 1 and system 2). defines a hyper-surface in the coordinate space of the composite system S(1+2) S(1+2) U (1,2) X = V, N 1, …N m – coordinates U of subsystems (1 and 2) X(1,2) (1,2) S – entropy of a composite system X U – energy of a composite system Notes Irreversible and reversible processes If we change constraints on some of the composite system coordinates, (e.g. -
Designing a Physics Learning Environment: a Holistic Approach
Designing a physics learning environment: A holistic approach David T. Brookes and Yuhfen Lin Department of Physics, Florida International University, 11200 SW 8th St, Miami, 33199 Abstract. Physics students enter our classroom with significant learning experiences and learning goals that are just as important as their prior knowledge. Consequently, they have expectations about how they should be taught. The instructor enters the same classroom and presents the students with materials and assessments that he/she believes reflect his/her learning goals for the students. When students encounter a reformed physics class, there is often a “misalignment” between students’ perceptions, and learning goals the instructor designed for the students. We want to propose that alignment can be achieved in a reformed physics class by taking a holistic view of the classroom. In other words, it is not just about teaching physics, but a problem of social engineering. We will discuss how we applied this social engineering idea on multiple scales (individual students, groups, and the whole class) to achieve alignment between students’ expectations and the instructor’s learning goals. Keywords: Physics education, learning environment, learning goals, attitudes, motivation PACS: 01.40.Fk, 01.40.Ha INTRODUCTION his/her students. 3) We paid careful attention to designing the learning environment to maximize Many Research-Based Instructional Strategies effective communication and interaction between (RBIS) in physics are initially successful when students. implemented by their developers, but other adopters sometimes struggle to achieve the same level of THEORY AND COURSE SETTING success. Firstly, students are resistant to reform [1]. Secondly, when physics instructors try implementing Interacting System Model one or more RBIS, they quickly discover that they do not work as advertised [2]. -
Lecture 24 Angular Momentum
LECTURE 24 ANGULAR MOMENTUM Instructor: Kazumi Tolich Lecture 24 2 ¨ Reading chapter 11-6 ¤ Angular momentum n Angular momentum about an axis n Newton’s 2nd law for rotational motion Angular momentum of an rotating object 3 ¨ An object with a moment of inertia of � about an axis rotates with an angular speed of � about the same axis has an angular momentum, �, given by � = �� ¤ This is analogous to linear momentum: � = �� Angular momentum in general 4 ¨ Angular momentum of a point particle about an axis is defined by � � = �� sin � = ��� sin � = �-� = ��. � �- ¤ �⃗: position vector for the particle from the axis. ¤ �: linear momentum of the particle: � = �� �⃗ ¤ � is moment arm, or sometimes called “perpendicular . Axis distance.” �. Quiz: 1 5 ¨ A particle is traveling in straight line path as shown in Case A and Case B. In which case(s) does the blue particle have non-zero angular momentum about the axis indicated by the red cross? A. Only Case A Case A B. Only Case B C. Neither D. Both Case B Quiz: 24-1 answer 6 ¨ Only Case A ¨ For a particle to have angular momentum about an axis, it does not have to be Case A moving in a circle. ¨ The particle can be moving in a straight path. Case B ¨ For it to have a non-zero angular momentum, its line of path is displaced from the axis about which the angular momentum is calculated. ¨ An object moving in a straight line that does not go through the axis of rotation has an angular position that changes with time. So, this object has an angular momentum. -
Rotational Motion and Angular Momentum 317
CHAPTER 10 | ROTATIONAL MOTION AND ANGULAR MOMENTUM 317 10 ROTATIONAL MOTION AND ANGULAR MOMENTUM Figure 10.1 The mention of a tornado conjures up images of raw destructive power. Tornadoes blow houses away as if they were made of paper and have been known to pierce tree trunks with pieces of straw. They descend from clouds in funnel-like shapes that spin violently, particularly at the bottom where they are most narrow, producing winds as high as 500 km/h. (credit: Daphne Zaras, U.S. National Oceanic and Atmospheric Administration) Learning Objectives 10.1. Angular Acceleration • Describe uniform circular motion. • Explain non-uniform circular motion. • Calculate angular acceleration of an object. • Observe the link between linear and angular acceleration. 10.2. Kinematics of Rotational Motion • Observe the kinematics of rotational motion. • Derive rotational kinematic equations. • Evaluate problem solving strategies for rotational kinematics. 10.3. Dynamics of Rotational Motion: Rotational Inertia • Understand the relationship between force, mass and acceleration. • Study the turning effect of force. • Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration. 10.4. Rotational Kinetic Energy: Work and Energy Revisited • Derive the equation for rotational work. • Calculate rotational kinetic energy. • Demonstrate the Law of Conservation of Energy. 10.5. Angular Momentum and Its Conservation • Understand the analogy between angular momentum and linear momentum. • Observe the relationship between torque and angular momentum. • Apply the law of conservation of angular momentum. 10.6. Collisions of Extended Bodies in Two Dimensions • Observe collisions of extended bodies in two dimensions. • Examine collision at the point of percussion. -
The Influence of Thermodynamic Ideas on Ecological Economics: an Interdisciplinary Critique
Sustainability 2009, 1, 1195-1225; doi:10.3390/su1041195 OPEN ACCESS sustainability ISSN 2071-1050 www.mdpi.com/journal/sustainability Article The Influence of Thermodynamic Ideas on Ecological Economics: An Interdisciplinary Critique Geoffrey P. Hammond 1,2,* and Adrian B. Winnett 1,3 1 Institute for Sustainable Energy & the Environment (I•SEE), University of Bath, Bath, BA2 7AY, UK 2 Department of Mechanical Engineering, University of Bath, Bath, BA2 7AY, UK 3 Department of Economics, University of Bath, Bath, BA2 7AY, UK; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +44-12-2538-6168; Fax: +44-12-2538-6928. Received: 10 October 2009 / Accepted: 24 November 2009 / Published: 1 December 2009 Abstract: The influence of thermodynamics on the emerging transdisciplinary field of ‗ecological economics‘ is critically reviewed from an interdisciplinary perspective. It is viewed through the lens provided by the ‗bioeconomist‘ Nicholas Georgescu-Roegen (1906–1994) and his advocacy of ‗the Entropy Law‘ as a determinant of economic scarcity. It is argued that exergy is a more easily understood thermodynamic property than is entropy to represent irreversibilities in complex systems, and that the behaviour of energy and matter are not equally mirrored by thermodynamic laws. Thermodynamic insights as typically employed in ecological economics are simply analogues or metaphors of reality. They should therefore be empirically tested against the real world. Keywords: thermodynamic analysis; energy; entropy; exergy; ecological economics; environmental economics; exergoeconomics; complexity; natural capital; sustainability Sustainability 2009, 1 1196 ―A theory is the more impressive, the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. -
Chapter 10 Energy and Work
Chapter 10 Energy and Work Lecture Presentation Chapter 10 Energy and Work Chapter Goal: To introduce the concept of energy and to learn a new problem-solving strategy based on conservation of energy. © 2015 Pearson Education, Inc. © 2015 Pearson Education, Inc. Slide 10-2 Chapter 10 Preview Chapter 10 Preview Looking Ahead: Forms of Energy Looking Ahead: Work and Energy • This dolphin has lots of kinetic energy as it leaves the • As the band is stretched, energy is transferred to it as water. At its highest point its energy is mostly potential work . This energy is then transformed into kinetic energy energy . of the rock. • You’ll learn about several of the most important forms of • You’ll learn how to calculate the work done by a force, energy—kinetic, potential, and thermal. and how this work is related to the change in a system’s energy. © 2015 Pearson Education, Inc. Slide 10-3 © 2015 Pearson Education, Inc. Slide 10-4 Chapter 10 Preview Chapter 10 Preview Looking Ahead: Conservation of Energy Looking Ahead • As they slide, their potential energy decreases and their kinetic energy increases, but their total energy is unchanged: It is conserved . • How fast will they be moving when they reach the bottom? Text: p. 283 You’ll use a new before-and-after analysis to find out. © 2015 Pearson Education, Inc. Slide 10-5 © 2015 Pearson Education, Inc. Slide 10-6 Chapter 10 Preview Chapter 10 Preview Looking Back: Motion with Constant Acceleration Stop to Think In Chapter 2 you learned how to describe the motion of a A car pulls away from a stop sign with a constant particle that has a constant acceleration. -
Sustainability and the Viable Systems Approach: Opportunities and Issues for the Governance of the Territory
sustainability Article Sustainability and the Viable Systems Approach: Opportunities and Issues for the Governance of the Territory Sergio Barile, Bernardino Quattrociocchi, Mario Calabrese ID and Francesca Iandolo * ID Department of Management, Sapienza University, Rome 00161, Italy; [email protected] (S.B.); [email protected] (B.Q.); [email protected] (M.C.) * Correspondence: [email protected] Received: 22 January 2018; Accepted: 3 March 2018; Published: 13 March 2018 Abstract: The aim of this paper is to propose an approach for representing the territory as a dynamic system of intersubjective relationships that is able to guarantee not only the efficiency of the processes within organizations, but also effective results in the general context and a sustainable impact on the broader environment. This contribution is developed on the basis of the viable systems approach (vSa), which is intended as a theoretical framework for the analysis of social phenomena as well as for orienting government processes. Using this theoretical framework, the proposed approach leads to the representation of the territory as a viable system that is capable of surviving in its own context by creating value for the other entities of the context (public groups of governments, communities, investors, natural environment, future generations, non-human species), thus defining the essential conditions for a sustainable equilibrium. The consideration that social phenomena have to be analyzed by taking into account the different relations and interactions that orient the behavior of individuals and, as a consequence, their main collective manifestations, i.e., organizations, underlines the importance of shifting from a traditional reductionist approach to a systemic approach. -
M34; Torque and Angular Momentum in Circular Motion
TORQUE AND ANGULAR MOMENTUM MISN-0-34 IN CIRCULAR MOTION by Kirby Morgan, Charlotte, Michigan TORQUE AND ANGULAR MOMENTUM 1. Introduction . 1 2. Torque and Angular Momentum IN CIRCULAR MOTION a. De¯nitions . 1 b. Relationship: ~¿ = dL=dt~ . .1 c. Motion Con¯ned to a Plane . 2 d. Circular Motion of a Mass . .3 3. Systems of Particles a. Total Angular Momentum . 4 shaft b. Total Torque . 4 c. Rigid Body Motion About a Fixed Axis . 5 d. Example: Flywheel . 5 e. Kinetic Energy of Rotation . 6 f. Linear vs. Rotational Motion . 6 4. Conservation of Angular Momentum a. Statement of the Law . 7 b. If the External Torque is not Zero . 7 c. Example: Two Flywheels . 7 d. Kinetic Energy of the Two Flywheels . 8 5. Nonplanar Rigid Bodies . 9 Acknowledgments. .9 Glossary . 9 Project PHYSNET·Physics Bldg.·Michigan State University·East Lansing, MI 1 2 ID Sheet: MISN-0-34 THIS IS A DEVELOPMENTAL-STAGE PUBLICATION Title: Torque and Angular Momentum in Circular Motion OF PROJECT PHYSNET Author: Kirby Morgan, HandiComputing, Charlotte, MI The goal of our project is to assist a network of educators and scientists in Version: 4/16/2002 Evaluation: Stage 0 transferring physics from one person to another. We support manuscript processing and distribution, along with communication and information Length: 1 hr; 24 pages systems. We also work with employers to identify basic scienti¯c skills Input Skills: as well as physics topics that are needed in science and technology. A number of our publications are aimed at assisting users in acquiring such 1.