III. Work and Energy
|
|
|
- Abigayle Lucas
- 5 years ago
- Views:
Transcription
1 Rotation I. Kinematics - Angular analogs II. III. IV. Dynamics - Torque and Rotational Inertia Work and Energy Angular Momentum - Bodies and particles V. Elliptical Orbits
2 The student will be able to: HW: 1 Define angular position, angular displacement, angular velocity, 1 5 angular acceleration and solve related problems in fixed axis kinematics. 2 Define torque, lever arm (moment arm), and solve related problems Define rotational inertia (moment of inertia), use provided formulas of 9 11 such to solve related problems. 4 Solve rotational dynamics problems using relation between torque, rotational inertia, and angular acceleration for fixed axis. 5 Define rotational kinetic energy and work and solve related problems Define angular momentum and angular impulse and solve related problems. 7 State and apply conservation of angular momentum to solve related problems. 8 Analyze orbital motion, including elliptical orbits, using conservation of angular momentum and energy.
3 Work, Energy, Power for Rotation The definitions and units for work, energy, and power do not change for rotational motion! Key difference is the relation of work to torque and the relation of kinetic energy to angular speed. The equations are just as expected using the analogous rotational quantities: W = τθ K = 1 2 Iω 2
4 Work, Energy, Power for Rotation The work energy theorem and conservation of energy are exactly the same! ΣW = ΔK ΣW NC +U 1 + K 1 =U 2 + K 2 W = τθ K = 1 2 Iω 2
5 Rotation I. Kinematics - Angular analogs II. III. IV. Dynamics - Torque and Rotational Inertia Work and Energy Angular Momentum - Bodies and particles V. Elliptical Orbits
6 The student will be able to: HW: 1 Define angular position, angular displacement, angular velocity, 1 5 angular acceleration and solve related problems in fixed axis kinematics. 2 Define torque, lever arm (moment arm), and solve related problems Define rotational inertia (moment of inertia), use provided formulas of 9 11 such to solve related problems. 4 Solve rotational dynamics problems using relation between torque, rotational inertia, and angular acceleration for fixed axis. 5 Define rotational kinetic energy and work and solve related problems Define angular momentum and angular impulse and solve related problems. 7 State and apply conservation of angular momentum to solve related problems. 8 Analyze orbital motion, including elliptical orbits, using conservation of angular momentum and energy.
7 Momentum and Impulse for Rotation Recall that linear momentum is the product of mass and velocity and that impulse is the product of force and time apply the analogous quantities of rotation to get the rotational equivalents. Recall that net force equals rate of change in linear momentum a similar statement can be made for torque and angular momentum. Recall that linear momentum is conserved when net external force is zero essentially the same can be said for angular momentum.
8 Angular Momentum is the product of rotational inertia and angular velocity.! L = I! ω Angular momentum is a vector in the same direction as angular velocity. Its magnitude has SI units of: kg m 2 /s.
9 Torque, Angular Momentum, Angular Impulse Starting with Newton s 2 nd Law for rotation it can be shown that net torque equals rate of change in angular momentum! τ! τ net net =! ΔL Δt! ( Δt) = ΔL which leads to a formula that equates net angular impulse with change in angular momentum.
10 Conservation of Angular Momentum The total angular momentum of an isolated system of objects will remain constant over time. For two objects that interact with one another:!!!! L + L = Lʹ + Lʹ !!!! I ω + I ω = I ωʹ + I ωʹ total angular momentum before an interaction total angular momentum after the interaction
11 Internal and External Torques In order for the total angular momentum of a particular system to remain constant there must be no net external torque on the system. When an object outside the system interacts with an object inside the system this is called external torque. When objects within a system interact with one another this is called internal torque. Internal torques have no effect on total angular momentum!
12 Rotation I. Kinematics - Angular analogs II. III. IV. Dynamics - Torque and Rotational Inertia Work and Energy Angular Momentum - Bodies and particles V. Elliptical Orbits
13 The student will be able to: HW: 1 Define angular position, angular displacement, angular velocity, 1 5 angular acceleration and solve related problems in fixed axis kinematics. 2 Define torque, lever arm (moment arm), and solve related problems Define rotational inertia (moment of inertia), use provided formulas of 9 11 such to solve related problems. 4 Solve rotational dynamics problems using relation between torque, rotational inertia, and angular acceleration for fixed axis. 5 Define rotational kinetic energy and work and solve related problems Define angular momentum and angular impulse and solve related problems. 7 State and apply conservation of angular momentum to solve related problems. 8 Analyze orbital motion, including elliptical orbits, using conservation of angular momentum and energy.
14 v r F a Special Focus: Elliptical Orbits r F v The position, r, velocity, v, and gravitational force, F, all vary in magnitude and direction as an object follows an elliptical orbit. The diagram illustrates the major axis, 2a, and the semi-major axis, a, of the ellipse. The value of a is usually referred to as the average distance between the two objects. (the symbol a does not represent acceleration in this diagram!) 2a This type of motion can be analyzed by using conservation of angular momentum and conservation of energy
15 Greater kinetic energy lower potential energy v r F Elliptical Orbits and Conservation Laws Angular momentum constant over entire orbit As shown in the figure the force of gravity acting on the satellite is always directed toward the central body. Taking the central body to be the axis of revolution there is zero torque due to gravity. Because there is no torque the angular momentum of the system remains constant. r F v Lower kinetic energy greater potential energy And because gravity is a conservative force and no other forces are signifcant the total mechanical energy of the system remains constant. As the satellite nears the central body it is like falling down and potential energy is converted to kinetic energy.
16 Elliptical Orbits and Angular Momentum The angular momentum should remain constant over the course of the entire orbit. Angular momentum is easiest to determine at the nearest and farthest points in the orbit. m v 1 r 1 r 2 m v 2 ( ) v r L = Iω = mr 2 L = rmv L = ʹ L r 1 mv 1 = r 2 mv 2 Angular momentum of satellite (r v) Note: finding angular momentum at any other point in the orbit is complicated by the fact that r and v are not perpendicular. Angular momentum nearest the central body Angular momentum farthest from central body
17 Elliptical Orbits and Angular Momentum The total mechanical energy of the system remains constant because only the conservative force of gravity acts. There is a special formula for this potential energy. v 1 r 1 a m U G = G Mm r Potential energy of the system M r 2 v 2 E =U 1 + K 1 =U 2ʹ + K 2ʹ G Mm + 1 r 1 2 mv 2 1 = G Mm + 1 r 2 2 mv 2 2 Note: the angles of r and v are do not affect energy and so this calculation can be done for any and every point in the orbit. E = G Mm 2a Total energy of the system
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 8-8: ANGULAR MOMENTUM AND ITS CONSERVATION Questions From Reading Activity? Big Idea(s): The interactions of an object with other objects can be
Rotation. I. Kinematics - Angular analogs
Rotation I. Kinematics - Angular analogs II. III. IV. Dynamics - Torque and Rotational Inertia Work and Energy Angular Momentum - Bodies and particles V. Elliptical Orbits The student will be able to:
Dynamics. Dynamics of mechanical particle and particle systems (many body systems)
Dynamics Dynamics of mechanical particle and particle systems (many body systems) Newton`s first law: If no net force acts on a body, it will move on a straight line at constant velocity or will stay at
Slide 1 / 37. Rotational Motion
Slide 1 / 37 Rotational Motion Slide 2 / 37 Angular Quantities An angle θ can be given by: where r is the radius and l is the arc length. This gives θ in radians. There are 360 in a circle or 2π radians.
Chapter 8. Rotational Motion
Chapter 8 Rotational Motion Rotational Work and Energy W = Fs = s = rθ Frθ Consider the work done in rotating a wheel with a tangential force, F, by an angle θ. τ = Fr W =τθ Rotational Work and Energy
Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and
Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about
Chapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics 9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination
Chapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular
Chapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.6 The Action of Forces and Torques on Rigid Objects Chapter 8 developed the concepts of angular motion. θ : angles and radian measure for angular variables ω :
Center of Gravity Pearson Education, Inc.
Center of Gravity = The center of gravity position is at a place where the torque from one end of the object is balanced by the torque of the other end and therefore there is NO rotation. Fulcrum Point
Chapter 8. Rotational Equilibrium and Rotational Dynamics
Chapter 8 Rotational Equilibrium and Rotational Dynamics 1 Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related 2 Torque The door is free to rotate
Chapter 8- Rotational Kinematics Angular Variables Kinematic Equations
Chapter 8- Rotational Kinematics Angular Variables Kinematic Equations Chapter 9- Rotational Dynamics Torque Center of Gravity Newton s 2 nd Law- Angular Rotational Work & Energy Angular Momentum Angular
AP Pd 3 Rotational Dynamics.notebook. May 08, 2014
1 Rotational Dynamics Why do objects spin? Objects can travel in different ways: Translation all points on the body travel in parallel paths Rotation all points on the body move around a fixed point An
= o + t = ot + ½ t 2 = o + 2
Chapters 8-9 Rotational Kinematics and Dynamics Rotational motion Rotational motion refers to the motion of an object or system that spins about an axis. The axis of rotation is the line about which the
CHAPTER 9 ROTATIONAL DYNAMICS
CHAPTER 9 ROTATIONAL DYNAMICS PROBLEMS. REASONING The drawing shows the forces acting on the person. It also shows the lever arms for a rotational axis perpendicular to the plane of the paper at the place
Chapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics 9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination
General Definition of Torque, final. Lever Arm. General Definition of Torque 7/29/2010. Units of Chapter 10
Units of Chapter 10 Determining Moments of Inertia Rotational Kinetic Energy Rotational Plus Translational Motion; Rolling Why Does a Rolling Sphere Slow Down? General Definition of Torque, final Taking
Application of Forces. Chapter Eight. Torque. Force vs. Torque. Torque, cont. Direction of Torque 4/7/2015
Raymond A. Serway Chris Vuille Chapter Eight Rotational Equilibrium and Rotational Dynamics Application of Forces The point of application of a force is important This was ignored in treating objects as
Chapter 8. Rotational Equilibrium and Rotational Dynamics
Chapter 8 Rotational Equilibrium and Rotational Dynamics Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related Torque The door is free to rotate about
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 8-5: ROTATIONAL DYNAMICS; TORQUE AND ROTATIONAL INERTIA LSN 8-6: SOLVING PROBLEMS IN ROTATIONAL DYNAMICS Questions From Reading Activity? Big Idea(s):
Rotational Dynamics continued
Chapter 9 Rotational Dynamics continued 9.4 Newton s Second Law for Rotational Motion About a Fixed Axis ROTATIONAL ANALOG OF NEWTON S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS I = ( mr 2
1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches
AP Physics B Practice Questions: Rotational Motion Multiple-Choice Questions 1. Which of the following is the unit for angular displacement? A. Meters B. Seconds C. Radians D. Radian per second E. Inches
Rotation of Rigid Objects
Notes 12 Rotation and Extended Objects Page 1 Rotation of Rigid Objects Real objects have "extent". The mass is spread out over discrete or continuous positions. THERE IS A DISTRIBUTION OF MASS TO "AN
Physics A - PHY 2048C
Physics A - PHY 2048C and 11/15/2017 My Office Hours: Thursday 2:00-3:00 PM 212 Keen Building Warm-up Questions 1 Did you read Chapter 12 in the textbook on? 2 Must an object be rotating to have a moment
Momentum Circular Motion and Gravitation Rotational Motion Fluid Mechanics
Momentum Circular Motion and Gravitation Rotational Motion Fluid Mechanics Momentum Momentum Collisions between objects can be evaluated using the laws of conservation of energy and of momentum. Momentum
31 ROTATIONAL KINEMATICS
31 ROTATIONAL KINEMATICS 1. Compare and contrast circular motion and rotation? Address the following Which involves an object and which involves a system? Does an object/system in circular motion have
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS AP PHYSICS LSN 8-7: ROTATIONAL KINETIC ENERGY Questions From Reading Activity? Big Idea(s): The interactions of an object with other objects can be described by
Work - kinetic energy theorem for rotational motion *
OpenStax-CNX module: m14307 1 Work - kinetic energy theorem for rotational motion * Sunil Kumar Singh This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 2.0
Northwestern Connecticut Community College Course Syllabus
Northwestern Connecticut Community College Course Syllabus Course Title: Introductory Physics Course #: PHY 110 Course Description: 4 credits (3 class hours and 3 laboratory hours per week) Physics 110
Rotation of Rigid Objects
Notes 12 Rotation and Extended Objects Page 1 Rotation of Rigid Objects Real objects have "extent". The mass is spread out over discrete or continuous positions. THERE IS A DISTRIBUTION OF MASS TO "AN
Lecture 14. Rotational dynamics Torque. Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
Lecture 14 Rotational dynamics Torque Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes, 87 1 BC EXAM Tuesday March 6, 018 8:15 PM 9:45 PM Today s Topics:
Chapter 8. Centripetal Force and The Law of Gravity
Chapter 8 Centripetal Force and The Law of Gravity Centripetal Acceleration An object traveling in a circle, even though it moves with a constant speed, will have an acceleration The centripetal acceleration
Broward County Schools AP Physics 1 Review
Broward County Schools AP Physics 1 Review 1 AP Physics 1 Review 1. The Basics of the Exam Important info: No penalty for guessing. Eliminate one or two choices and then take a shot. Multi-select questions
Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics
Circular Motion, Pt 2: Angular Dynamics Mr. Velazquez AP/Honors Physics Formulas: Angular Kinematics (θ must be in radians): s = rθ Arc Length 360 = 2π rads = 1 rev ω = θ t = v t r Angular Velocity α av
Angular Momentum. Objectives CONSERVATION OF ANGULAR MOMENTUM
Angular Momentum CONSERVATION OF ANGULAR MOMENTUM Objectives Calculate the angular momentum vector for a moving particle Calculate the angular momentum vector for a rotating rigid object where angular
Chapter 9. Rotational Dynamics
Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular
PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2)
PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2) We will limit our study of planar kinetics to rigid bodies that are symmetric with respect to a fixed reference plane. As discussed in Chapter 16, when
AP PHYSICS 1 Learning Objectives Arranged Topically
AP PHYSICS 1 Learning Objectives Arranged Topically with o Big Ideas o Enduring Understandings o Essential Knowledges o Learning Objectives o Science Practices o Correlation to Knight Textbook Chapters
Chapter 8. Rotational Equilibrium and Rotational Dynamics
Chapter 8 Rotational Equilibrium and Rotational Dynamics Wrench Demo Torque Torque, τ, is the tendency of a force to rotate an object about some axis τ = Fd F is the force d is the lever arm (or moment
Chapter 8. Rotational Equilibrium and Rotational Dynamics. 1. Torque. 2. Torque and Equilibrium. 3. Center of Mass and Center of Gravity
Chapter 8 Rotational Equilibrium and Rotational Dynamics 1. Torque 2. Torque and Equilibrium 3. Center of Mass and Center of Gravity 4. Torque and angular acceleration 5. Rotational Kinetic energy 6. Angular
Rigid Body Dynamics and Beyond
Rigid Body Dynamics and Beyond 1 Rigid Bodies 3 A rigid body Collection of particles Distance between any two particles is always constant What types of motions preserve these constraints? Translation,
DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS BADDEST CLASS ON CAMPUS IB PHYSICS OPTION B-1A: ROTATIONAL DYNAMICS Essential Idea: The basic laws of mechanics have an extension when equivalent principles are applied to rotation. Actual
Rotational Motion. Every quantity that we have studied with translational motion has a rotational counterpart
Rotational Motion & Angular Momentum Rotational Motion Every quantity that we have studied with translational motion has a rotational counterpart TRANSLATIONAL ROTATIONAL Displacement x Angular Displacement
ω = 0 a = 0 = α P = constant L = constant dt = 0 = d Equilibrium when: τ i = 0 τ net τ i Static Equilibrium when: F z = 0 F net = F i = ma = d P
Equilibrium when: F net = F i τ net = τ i a = 0 = α dp = 0 = d L = ma = d P = 0 = I α = d L = 0 P = constant L = constant F x = 0 τ i = 0 F y = 0 F z = 0 Static Equilibrium when: P = 0 L = 0 v com = 0
Ch 8. Rotational Dynamics
Ch 8. Rotational Dynamics Rotational W, P, K, & L (a) Translation (b) Combined translation and rotation ROTATIONAL ANALOG OF NEWTON S SECOND LAW FOR A RIGID BODY ROTATING ABOUT A FIXED AXIS = τ Iα Requirement:
= 2 5 MR2. I sphere = MR 2. I hoop = 1 2 MR2. I disk
A sphere (green), a disk (blue), and a hoop (red0, each with mass M and radius R, all start from rest at the top of an inclined plane and roll to the bottom. Which object reaches the bottom first? (Use
Chapter 8 Lecture Notes
Chapter 8 Lecture Notes Physics 2414 - Strauss Formulas: v = l / t = r θ / t = rω a T = v / t = r ω / t =rα a C = v 2 /r = ω 2 r ω = ω 0 + αt θ = ω 0 t +(1/2)αt 2 θ = (1/2)(ω 0 +ω)t ω 2 = ω 0 2 +2αθ τ
PHYSICS 220. Lecture 15. Textbook Sections Lecture 15 Purdue University, Physics 220 1
PHYSICS 220 Lecture 15 Angular Momentum Textbook Sections 9.3 9.6 Lecture 15 Purdue University, Physics 220 1 Last Lecture Overview Torque = Force that causes rotation τ = F r sin θ Work done by torque
Northwestern CT Community College Course Syllabus. Course Title: CALCULUS-BASED PHYSICS I with Lab Course #: PHY 221
Northwestern CT Community College Course Syllabus Course Title: CALCULUS-BASED PHYSICS I with Lab Course #: PHY 221 Course Description: 4 credits (3 class hours and 3 laboratory hours per week) Physics
CIRCULAR MOTION AND ROTATION
1. UNIFORM CIRCULAR MOTION So far we have learned a great deal about linear motion. This section addresses rotational motion. The simplest kind of rotational motion is an object moving in a perfect circle
Rotational Kinematics
Rotational Kinematics Rotational Coordinates Ridged objects require six numbers to describe their position and orientation: 3 coordinates 3 axes of rotation Rotational Coordinates Use an angle θ to describe
Chapter 8: Momentum, Impulse, & Collisions. Newton s second law in terms of momentum:
linear momentum: Chapter 8: Momentum, Impulse, & Collisions Newton s second law in terms of momentum: impulse: Under what SPECIFIC condition is linear momentum conserved? (The answer does not involve collisions.)
Topic 1: Newtonian Mechanics Energy & Momentum
Work (W) the amount of energy transferred by a force acting through a distance. Scalar but can be positive or negative ΔE = W = F! d = Fdcosθ Units N m or Joules (J) Work, Energy & Power Power (P) the
Physics 2A Chapter 10 - Rotational Motion Fall 2018
Physics A Chapter 10 - Rotational Motion Fall 018 These notes are five pages. A quick summary: The concepts of rotational motion are a direct mirror image of the same concepts in linear motion. Follow
Chapter 9- Static Equilibrium
Chapter 9- Static Equilibrium Changes in Office-hours The following changes will take place until the end of the semester Office-hours: - Monday, 12:00-13:00h - Wednesday, 14:00-15:00h - Friday, 13:00-14:00h
Kinetic Energy of Rolling
Kinetic Energy of Rolling A solid disk and a hoop (with the same mass and radius) are released from rest and roll down a ramp from a height h. Which one is moving faster at the bottom of the ramp? A. they
10-6 Angular Momentum and Its Conservation [with Concept Coach]
![10-6 Angular Momentum and Its Conservation [with Concept Coach]](/thumbs/78/77902480.jpg "10-6 Angular Momentum and Its Conservation [with Concept Coach]")
OpenStax-CNX module: m50810 1 10-6 Angular Momentum and Its Conservation [with Concept Coach] OpenStax Tutor Based on Angular Momentum and Its Conservation by OpenStax College This work is produced by
Rotational Motion. Chapter 8: Rotational Motion. Angular Position. Rotational Motion. Ranking: Rolling Cups 9/21/12
Rotational Motion Chapter 8: Rotational Motion In physics we distinguish two types of motion for objects: Translational Motion (change of location): Whole object moves through space. Rotational Motion
Lecture PowerPoints. Chapter 8 Physics: Principles with Applications, 6 th edition Giancoli
Lecture PowerPoints Chapter 8 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the
Textbook Reference: Wilson, Buffa, Lou: Chapter 8 Glencoe Physics: Chapter 8
AP Physics Rotational Motion Introduction: Which moves with greater speed on a merry-go-round - a horse near the center or one near the outside? Your answer probably depends on whether you are considering
Motion in Space. MATH 311, Calculus III. J. Robert Buchanan. Fall Department of Mathematics. J. Robert Buchanan Motion in Space
Motion in Space MATH 311, Calculus III J. Robert Buchanan Department of Mathematics Fall 2011 Background Suppose the position vector of a moving object is given by r(t) = f (t), g(t), h(t), Background
Rotational Dynamics. A wrench floats weightlessly in space. It is subjected to two forces of equal and opposite magnitude: Will the wrench accelerate?
Rotational Dynamics A wrench floats weightlessly in space. It is subjected to two forces of equal and opposite magnitude: Will the wrench accelerate? A. yes B. no C. kind of? Rotational Dynamics 10.1-3
Chapter 9-10 Test Review
Chapter 9-10 Test Review Chapter Summary 9.2. The Second Condition for Equilibrium Explain torque and the factors on which it depends. Describe the role of torque in rotational mechanics. 10.1. Angular
Physics 1A. Lecture 8A
Physics 1A Lecture 8A Review of Last Lecture A closed system is one which does not exchange (mechanical) energy with its environment total mechanical energy is conserved in this system Force is the negative
Lecture 13 REVIEW. Physics 106 Spring What should we know? What should we know? Newton s Laws
Lecture 13 REVIEW Physics 106 Spring 2006 http://web.njit.edu/~sirenko/ What should we know? Vectors addition, subtraction, scalar and vector multiplication Trigonometric functions sinθ, cos θ, tan θ,
Rotational Motion About a Fixed Axis
Rotational Motion About a Fixed Axis Vocabulary rigid body axis of rotation radian average angular velocity instantaneous angular average angular Instantaneous angular frequency velocity acceleration acceleration
Review for 3 rd Midterm
Review for 3 rd Midterm Midterm is on 4/19 at 7:30pm in the same rooms as before You are allowed one double sided sheet of paper with any handwritten notes you like. The moment-of-inertia about the center-of-mass
8 Rotational motion of solid objects
8 Rotational motion of solid objects Kinematics of rotations PHY166 Fall 005 In this Lecture we call solid objects such extended objects that are rigid (nondeformable) and thus retain their shape. In contrast
Chapter 11. Angular Momentum
Chapter 11 Angular Momentum Angular Momentum Angular momentum plays a key role in rotational dynamics. There is a principle of conservation of angular momentum. In analogy to the principle of conservation
Rotational Dynamics, Moment of Inertia and Angular Momentum
Rotational Dynamics, Moment of Inertia and Angular Momentum Now that we have examined rotational kinematics and torque we will look at applying the concepts of angular motion to Newton s first and second
Torque and Rotation Lecture 7
Torque and Rotation Lecture 7 ˆ In this lecture we finally move beyond a simple particle in our mechanical analysis of motion. ˆ Now we consider the so-called rigid body. Essentially, a particle with extension
Dynamics of Rotational Motion
Chapter 10 Dynamics of Rotational Motion To understand the concept of torque. To relate angular acceleration and torque. To work and power in rotational motion. To understand angular momentum. To understand
Kinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)
Kinematics (special case) a = constant 1D motion 2D projectile Uniform circular Dynamics gravity, tension, elastic, normal, friction Motion with a = constant Newton s Laws F = m a F 12 = F 21 Time & Position
Ph1a: Solution to the Final Exam Alejandro Jenkins, Fall 2004
Ph1a: Solution to the Final Exam Alejandro Jenkins, Fall 2004 Problem 1 (10 points) - The Delivery A crate of mass M, which contains an expensive piece of scientific equipment, is being delivered to Caltech.
Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion. Torque and angular momentum
Handout 7: Torque, angular momentum, rotational kinetic energy and rolling motion Torque and angular momentum In Figure, in order to turn a rod about a fixed hinge at one end, a force F is applied at a
Physics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy
ics Tuesday, ember 2, 2002 Ch 11: Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy Announcements Wednesday, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468 Announcements This
Chapter 10 Rotational Kinematics and Energy. Copyright 2010 Pearson Education, Inc.
Chapter 10 Rotational Kinematics and Energy Copyright 010 Pearson Education, Inc. 10-1 Angular Position, Velocity, and Acceleration Copyright 010 Pearson Education, Inc. 10-1 Angular Position, Velocity,
Angular Momentum L = I ω
Angular Momentum L = Iω If no NET external Torques act on a system then Angular Momentum is Conserved. Linitial = I ω = L final = Iω Angular Momentum L = Iω Angular Momentum L = I ω A Skater spins with
Chapter 8. Rotational Motion
Chapter 8 Rotational Motion The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of
GIANCOLI READING ACTIVITY Lesson 8-4
AP PHYSICS Name: Period: Date: DEVIL PHYSICS BADDEST CLASS ON CAMPUS 1. Big Idea(s): GIANCOLI READING ACTIVITY Lesson 8-4 a. Big Idea 3: The interactions of an object with other objects can be described
Gyroscopes and statics
Gyroscopes and statics Announcements: Welcome back from Spring Break! CAPA due Friday at 10pm We will finish Chapter 11 in H+R on angular momentum and start Chapter 12 on stability. Friday we will begin
Physics 4A Solutions to Chapter 10 Homework
Physics 4A Solutions to Chapter 0 Homework Chapter 0 Questions: 4, 6, 8 Exercises & Problems 6, 3, 6, 4, 45, 5, 5, 7, 8 Answers to Questions: Q 0-4 (a) positive (b) zero (c) negative (d) negative Q 0-6
Lab 11: Rotational Dynamics
Lab 11: Rotational Dynamics Objectives: To understand the relationship between net torque and angular acceleration. To understand the concept of the moment of inertia. To understand the concept of angular
Rotational N.2 nd Law
Lecture 0 Chapter 1 Physics I Rotational N. nd Law Torque Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational dynamics Today
Axis Balanced Forces Centripetal force. Change in velocity Circular Motion Circular orbit Collision. Conservation of Energy
When something changes its velocity The rate of change of velocity of a moving object. Can result from a change in speed and/or a change in direction On surface of earth, value is 9.8 ms-²; increases nearer
Rolling without slipping Angular Momentum Conservation of Angular Momentum. Physics 201: Lecture 19, Pg 1
Physics 131: Lecture Today s Agenda Rolling without slipping Angular Momentum Conservation o Angular Momentum Physics 01: Lecture 19, Pg 1 Rolling Without Slipping Rolling is a combination o rotation and
Recap: Solid Rotational Motion (Chapter 8) displacement velocity acceleration Newton s 2nd law τ = I.α N.s τ = F. l moment of inertia mass size
Recap: Solid Rotational Motion (Chapter 8) We have developed equations to describe rotational displacement θ, rotational velocity ω and rotational acceleration α. We have used these new terms to modify
Solutions to Exam #1
SBCC 2017Summer2 P 101 Solutions to Exam 01 2017Jul11A Page 1 of 9 Solutions to Exam #1 1. Which of the following natural sciences most directly involves and applies physics? a) Botany (plant biology)
Rotational Motion and Torque
Rotational Motion and Torque Introduction to Angular Quantities Sections 8- to 8-2 Introduction Rotational motion deals with spinning objects, or objects rotating around some point. Rotational motion is
Angular Momentum L = I ω
Angular Momentum L = Iω If no NET external Torques act on a system then Angular Momentum is Conserved. Linitial = I ω = L final = Iω Angular Momentum L = Iω Angular Momentum L = I ω A Skater spins with
r CM = ir im i i m i m i v i (2) P = i
Physics 121 Test 3 study guide Thisisintendedtobeastudyguideforyourthirdtest, whichcoverschapters 9, 10, 12, and 13. Note that chapter 10 was also covered in test 2 without section 10.7 (elastic collisions),
Lesson 7. Luis Anchordoqui. Physics 168. Tuesday, October 10, 17
Lesson 7 Physics 168 1 Eruption of a large volcano on Jupiter s moon When volcano erupts speed of effluence exceeds escape speed of Io and so a stream of particles is projected into space Material in stream
Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1
Physics 201 p. 1/1 Physics 201 Professor P. Q. Hung 311B, Physics Building Physics 201 p. 2/1 Rotational Kinematics and Energy Rotational Kinetic Energy, Moment of Inertia All elements inside the rigid
Chapter 8 Lecture. Pearson Physics. Rotational Motion and Equilibrium. Prepared by Chris Chiaverina Pearson Education, Inc.
Chapter 8 Lecture Pearson Physics Rotational Motion and Equilibrium Prepared by Chris Chiaverina Chapter Contents Describing Angular Motion Rolling Motion and the Moment of Inertia Torque Static Equilibrium
PHY131H1S - Class 20. Pre-class reading quiz on Chapter 12
PHY131H1S - Class 20 Today: Gravitational Torque Rotational Kinetic Energy Rolling without Slipping Equilibrium with Rotation Rotation Vectors Angular Momentum Pre-class reading quiz on Chapter 12 1 Last
PH 221-3A Fall 2009 ROTATION. Lectures Chapter 10 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition)
PH 1-3A Fall 009 ROTATION Lectures 16-17 Chapter 10 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 10 Rotation In this chapter we will study the rotational motion of rigid bodies
Chapter 8 Rotational Motion and Equilibrium
Chapter 8 Rotational Motion and Equilibrium 8.1 Rigid Bodies, Translations, and Rotations A rigid body is an object or a system of particles in which the distances between particles are fixed (remain constant).
Translational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work
Translational vs Rotational / / 1/ Δ m x v dx dt a dv dt F ma p mv KE mv Work Fd / / 1/ θ ω θ α ω τ α ω ω τθ Δ I d dt d dt I L I KE I Work / θ ω α τ Δ Δ c t s r v r a v r a r Fr L pr Connection Translational
Physics 218 Exam 3 Spring 2010, Sections
Physics 8 Exam 3 Spring 00, Sections 5-55 Do not fill out the information below until instructed to do so! Name Signature Student ID E-mail Section # Rules of the exam:. You have the full class period
A. Incorrect! It looks like you forgot to include π in your calculation of angular velocity.
High School Physics - Problem Drill 10: Rotational Motion and Equilbrium 1. If a bike wheel of radius 50 cm rotates at 300 rpm what is its angular velocity and what is the linear speed of a point on the