Momentum. The way to catch a knuckleball is to wait until it stops rolling and then pick it up. -Bob Uecker
|
|
|
- Katrina Young
- 6 years ago
- Views:
Transcription
1 Chapter 11 -, Chapter 11 -, Angular The way to catch a knuckleball is to wait until it stops rolling and then pick it up. -Bob Uecker David J. Starling Penn State Hazleton PHYS 211
2 Chapter 11 -, motion is a combination of pure rotation and pure translation. Angular
3 Chapter 11 -, motion is a combination of pure rotation and pure translation. Angular
4 Chapter 11 -, motion is a combination of pure rotation and pure translation. Angular
5 Chapter 11 -, motion is a combination of pure rotation and pure translation. Angular Each velocity vector on the wheel is a sum of v com and the rotation.
6 Chapter 11 -, The relationship between the angular and linear velocities is fixed if the wheel does not slip. v com = Rω Angular
7 Chapter 11 -, The relationship between the angular and linear velocities is fixed if the wheel does not slip. v com = Rω Angular Note: therefore, a com = Rα.
8 Chapter 11 -, If the rolling object does not slip, then the point in contact with the floor is momentarily stationary. Angular
9 Chapter 11 -, If the rolling object does not slip, then the point in contact with the floor is momentarily stationary. Angular In this case, there is a static force of friction at the pivot that does no work.
10 Chapter 11 -, The kinetic energy of the wheel rotating about point P is Angular K = 1 2 I pω 2
11 Chapter 11 -, The kinetic energy of the wheel rotating about point P is Angular K = 1 2 I pω 2 = 1 ( Icom + MR 2) ω 2 2
12 Chapter 11 -, The kinetic energy of the wheel rotating about point P is Angular K = 1 2 I pω 2 = 1 ( Icom + MR 2) ω 2 2 = 1 2 I comω M(Rω)2
13 Chapter 11 -, The kinetic energy of the wheel rotating about point P is Angular K = 1 2 I pω 2 = 1 ( Icom + MR 2) ω 2 2 = 1 2 I comω M(Rω)2 = 1 2 I comω Mv2
14 Chapter 11 -, The kinetic energy of the wheel rotating about point P is Angular K = 1 2 I pω 2 = 1 ( Icom + MR 2) ω 2 2 = 1 2 I comω M(Rω)2 = 1 2 I comω Mv2 K = K R + K T
15 Chapter 11 -, When a rolling object accelerates, the friction force opposes the tendency to slip. Angular
16 Chapter 11 -, When a rolling object accelerates, the friction force opposes the tendency to slip. Angular Notice how the force does not oppose the direction of motion!
17 Chapter 11 -, Lecture Question 11.1 Which one of the following statements concerning a wheel undergoing rolling motion is true? (a) The angular acceleration of the wheel must be 0 m/s 2. (b) The tangential velocity is the same for all points on the wheel. (c) The linear velocity for all points on the rim of the wheel is non-zero. (d) The tangential velocity is the same for all points on the rim of the wheel. (e) There is no slipping at the point where the wheel touches the surface on which it is rolling. Angular
18 Angular Chapter 11 -, An object A with momentum p also has angular momentum l = r p about some point O. Angular
19 Angular Chapter 11 -, An object A with momentum p also has angular momentum l = r p about some point O. Angular Why is it defined this way?
20 Angular Chapter 11 -, From Newton s 2nd Law, let s take a derivative of this momentum : Angular d l dt = d ( r p) dt
21 Angular Chapter 11 -, From Newton s 2nd Law, let s take a derivative of this momentum : Angular d l dt = d ( r p) dt = d r d p p + r dt dt
22 Angular Chapter 11 -, From Newton s 2nd Law, let s take a derivative of this momentum : Angular d l dt = d ( r p) dt = d r d p p + r dt dt = v p + r (m a)
23 Angular Chapter 11 -, From Newton s 2nd Law, let s take a derivative of this momentum : Angular d l dt = d ( r p) dt = d r d p p + r dt dt = v p + r (m a) = r F net
24 Angular Chapter 11 -, From Newton s 2nd Law, let s take a derivative of this momentum : Angular d l dt = d ( r p) dt = d r d p p + r dt dt = v p + r (m a) = r F net = τ net
25 Angular Chapter 11 -, From Newton s 2nd Law, let s take a derivative of this momentum : Angular d l dt = d ( r p) dt = d r d p p + r dt dt = v p + r (m a) = r F net = τ net τ net = d l dt
26 Angular Chapter 11 -, If there is more than one particle, the total angular momentum L is just the vector sum of the individual angular momentums l i. Angular L = l 1 + l l N = N l i i=1 And the net torque on the whole system is just: τ net = d L dt
27 Angular The angular momentum of a rigid body can be found by adding up the angular momentum of the particles that make it up: Chapter 11 -, Angular l i = r i p i = r i m i v i
28 Angular Chapter 11 -, Angular l i = r i m i v i
29 Angular Chapter 11 -, Angular l i = r i m i v i = r i m i (r i ω)
30 Angular Chapter 11 -, Angular l i = r i m i v i = r i m i (r i ω) = ( m i r 2 i )ω
31 Angular Chapter 11 -, Angular l i = r i m i v i = r i m i (r i ω) = ( m i r 2 i )ω L = i ( m i r 2 i )ω
32 Angular Chapter 11 -, Angular l i = r i m i v i = r i m i (r i ω) = ( m i r 2 i )ω L = ( m i r i 2 )ω i ( ) = m i r i 2 ω i
33 Angular Chapter 11 -, Angular l i = r i m i v i = r i m i (r i ω) = ( m i r 2 i )ω L = ( m i r i 2 )ω i ( ) = m i r i 2 ω L = I ω i
34 Angular Chapter 11 -, There are many similarities between linear and angular momentum. Angular
35 Angular Chapter 11 -, Lecture Question 11.2 What is the direction of the Earth s angular momentum as it spins about its axis? (a) north (b) south (c) east (d) west (e) radially inward Angular
36 If the net external torque on a system is zero, the angular momentum is conserved. τ net = d L dt = 0 L = constant Chapter 11 -, Angular
37 If the net external torque on a system is zero, the angular momentum is conserved. τ net = d L dt = 0 L = constant Chapter 11 -, Angular
38 A gyroscope is an object that spins very quickly. Such an object behaves obeys the angular Newton s Second Law. Chapter 11 -, Angular τ = d L dt
39 A gyroscope is an object that spins very quickly. Such an object behaves obeys the angular Newton s Second Law. Chapter 11 -, Angular τ = d L dt
40 A gyroscope is an object that spins very quickly. Such an object behaves obeys the angular Newton s Second Law. Chapter 11 -, Angular τ = d L dt
41 When a gyroscope is subjected to a gravitational force it precesses. Chapter 11 -, Angular
42 When a gyroscope is subjected to a gravitational force it precesses. Chapter 11 -, Angular τ = d L dt
43 When a gyroscope is subjected to a gravitational force it precesses. Chapter 11 -, Angular τ = d L dt dl = τ dt = Mgr dt
44 When a gyroscope is subjected to a gravitational force it precesses. Chapter 11 -, Angular τ = d L dt dl = τ dt = Mgr dt dφ = dl Mgr dt = L Iω
45 When a gyroscope is subjected to a gravitational force it precesses. Chapter 11 -, Angular τ = d L dt dl = τ dt = Mgr dt dφ = dl L dφ dt = Mgr Iω = Mgr dt Iω (rate of precession)
46 Chapter 11 -, Lecture Question 11.3 A solid sphere of radius R rotates about an axis that is tangent to the sphere with an angular speed ω. Under the action of internal forces, the radius of the sphere increases to 2R. What is the final angular speed of the sphere? (a) ω/4 (b) ω/2 (c) ω (d) 2ω (e) 4ω Angular
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
Lecture 6 Physics 106 Spring 2006
Lecture 6 Physics 106 Spring 2006 Angular Momentum Rolling Angular Momentum: Definition: Angular Momentum for rotation System of particles: Torque: l = r m v sinφ l = I ω [kg m 2 /s] http://web.njit.edu/~sirenko/
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
Plane Motion of Rigid Bodies: Momentum Methods
Plane Motion of Rigid Bodies: Momentum Methods Reference: Beer, Ferdinand P. et al, Vector Mechanics for Engineers : Dynamics, 8 th Edition, Mc GrawHill Hibbeler R.C., Engineering Mechanics: Dynamics,
Rolling, Torque, Angular Momentum
Chapter 11 Rolling, Torque, Angular Momentum Copyright 11.2 Rolling as Translational and Rotation Combined Motion of Translation : i.e.motion along a straight line Motion of Rotation : rotation about a
Torque. Introduction. Torque. PHY torque - J. Hedberg
Torque PHY 207 - torque - J. Hedberg - 2017 1. Introduction 2. Torque 1. Lever arm changes 3. Net Torques 4. Moment of Rotational Inertia 1. Moment of Inertia for Arbitrary Shapes 2. Parallel Axis Theorem
Physics 121, March 25, Rotational Motion and Angular Momentum. Department of Physics and Astronomy, University of Rochester
Physics 121, March 25, 2008. Rotational Motion and Angular Momentum. Physics 121. March 25, 2008. Course Information Topics to be discussed today: Review of Rotational Motion Rolling Motion Angular Momentum
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
Q1. For a completely inelastic two-body collision the kinetic energy of the objects after the collision is the same as:
Coordinator: Dr.. Naqvi Monday, January 05, 015 Page: 1 Q1. For a completely inelastic two-body collision the kinetic energy of the objects after the collision is the same as: ) (1/) MV, where M is the
Lecture 2- Rotation Chapter 11
Course Comments Rolling: Translation+Rotation Forces and Kinetic Energy Torque+vectors Angular Momentum Yo-Yo 1 / 8 Lecture 2- Rotation Chapter 11 Prof. Noronha-Hostler PHY-124H HONOROS ANALYTICAL PHYSICS
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
Chapter 11. Angular Momentum
Chapter 11 Angular Momentum Angular Momentum The Vector Nature of Rotation Torque and Angular Momentum Conservation of Angular Momentum MFMcGraw-PHY 2425 Chap_11Ha_Angular_Momentum-Revised 10/13/2012 2
= 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
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 PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Learning Goals for Chapter 10 Looking forward
7. The gyroscope. 7.1 Introduction. 7.2 Theory. a) The gyroscope
K 7. The gyroscope 7.1 Introduction This experiment concerns a special type of motion of a gyroscope, called precession. From the angular frequency of the precession, the moment of inertia of the spinning
Physics 141. Lecture 18. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 18, Page 1
Physics 141. Lecture 18. Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester, Lecture 18, Page 1 Physics 141. Lecture 18. Course Information. Topics to be discussed today: A
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.)
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
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
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
Physics Fall Mechanics, Thermodynamics, Waves, Fluids. Lecture 20: Rotational Motion. Slide 20-1
Physics 1501 Fall 2008 Mechanics, Thermodynamics, Waves, Fluids Lecture 20: Rotational Motion Slide 20-1 Recap: center of mass, linear momentum A composite system behaves as though its mass is concentrated
Test 7 wersja angielska
Test 7 wersja angielska 7.1A One revolution is the same as: A) 1 rad B) 57 rad C) π/2 rad D) π rad E) 2π rad 7.2A. If a wheel turns with constant angular speed then: A) each point on its rim moves with
A B Ax Bx Ay By Az Bz
Lecture 5.1 Dynamics of Rotation For some time now we have been discussing the laws of classical dynamics. However, for the most part, we only talked about examples of translational motion. On the other
Rotational Kinematics and Dynamics. UCVTS AIT Physics
Rotational Kinematics and Dynamics UCVTS AIT Physics Angular Position Axis of rotation is the center of the disc Choose a fixed reference line Point P is at a fixed distance r from the origin Angular Position,
Physics 121, March 27, Angular Momentum, Torque, and Precession. Department of Physics and Astronomy, University of Rochester
Physics 121, March 27, 2008. Angular Momentum, Torque, and Precession. Physics 121. March 27, 2008. Course Information Quiz Topics to be discussed today: Review of Angular Momentum Conservation of Angular
Two-Dimensional Rotational Kinematics
Two-Dimensional Rotational Kinematics Rigid Bodies A rigid body is an extended object in which the distance between any two points in the object is constant in time. Springs or human bodies are non-rigid
Rotational Dynamics. Slide 2 / 34. Slide 1 / 34. Slide 4 / 34. Slide 3 / 34. Slide 6 / 34. Slide 5 / 34. Moment of Inertia. Parallel Axis Theorem
Slide 1 / 34 Rotational ynamics l Slide 2 / 34 Moment of Inertia To determine the moment of inertia we divide the object into tiny masses of m i a distance r i from the center. is the sum of all the tiny
Rolling, Torque, and Angular Momentum
AP Physics C Rolling, Torque, and Angular Momentum Introduction: Rolling: In the last unit we studied the rotation of a rigid body about a fixed axis. We will now extend our study to include cases where
Chapter 10. Rotation of a Rigid Object about a Fixed Axis
Chapter 10 Rotation of a Rigid Object about a Fixed Axis Angular Position Axis of rotation is the center of the disc Choose a fixed reference line. Point P is at a fixed distance r from the origin. A small
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
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
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
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
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
Physics 131: Lecture 22. Today s Agenda
Physics 131: Lecture Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 01: Lecture 10, Pg 1 An Unfair Race A frictionless block and a rolling (without slipping) disk are released at
Forces of Rolling. 1) Ifobjectisrollingwith a com =0 (i.e.no netforces), then v com =ωr = constant (smooth roll)
Physics 2101 Section 3 March 12 rd : Ch. 10 Announcements: Mid-grades posted in PAW Quiz today I will be at the March APS meeting the week of 15-19 th. Prof. Rich Kurtz will help me. Class Website: http://www.phys.lsu.edu/classes/spring2010/phys2101-3/
Chapter 10: Dynamics of Rotational Motion
Chapter 10: Dynamics of Rotational Motion What causes an angular acceleration? The effectiveness of a force at causing a rotation is called torque. QuickCheck 12.5 The four forces shown have the same strength.
Physics 131: Lecture 22. Today s Agenda
Physics 131: Lecture 22 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 201: Lecture 10, Pg 1 An Unfair Race A frictionless block and a rolling (without slipping) disk are released
I 2 comω 2 + Rolling translational+rotational. a com. L sinθ = h. 1 tot. smooth rolling a com =αr & v com =ωr
Rolling translational+rotational smooth rolling a com =αr & v com =ωr Equations of motion from: - Force/torque -> a and α - Energy -> v and ω 1 I 2 comω 2 + 1 Mv 2 = KE 2 com tot a com KE tot = KE trans
Concept Question: Normal Force
Concept Question: Normal Force Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical
Rolling, Torque & Angular Momentum
PHYS 101 Previous Exam Problems CHAPTER 11 Rolling, Torque & Angular Momentum Rolling motion Torque Angular momentum Conservation of angular momentum 1. A uniform hoop (ring) is rolling smoothly from the
11-2 A General Method, and Rolling without Slipping
11-2 A General Method, and Rolling without Slipping Let s begin by summarizing a general method for analyzing situations involving Newton s Second Law for Rotation, such as the situation in Exploration
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
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
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,
Physics 141 Rotational Motion 2 Page 1. Rotational Motion 2
Physics 141 Rotational Motion 2 Page 1 Rotational Motion 2 Right handers, go over there, left handers over here. The rest of you, come with me.! Yogi Berra Torque Motion of a rigid body, like motion of
1.1. Rotational Kinematics Description Of Motion Of A Rotating Body
PHY 19- PHYSICS III 1. Moment Of Inertia 1.1. Rotational Kinematics Description Of Motion Of A Rotating Body 1.1.1. Linear Kinematics Consider the case of linear kinematics; it concerns the description
Angular velocity and angular acceleration CHAPTER 9 ROTATION. Angular velocity and angular acceleration. ! equations of rotational motion
Angular velocity and angular acceleration CHAPTER 9 ROTATION! r i ds i dθ θ i Angular velocity and angular acceleration! equations of rotational motion Torque and Moment of Inertia! Newton s nd Law for
ω avg [between t 1 and t 2 ] = ω(t 1) + ω(t 2 ) 2
![ω avg [between t 1 and t 2 ] = ω(t 1) + ω(t 2 ) 2](/thumbs/94/120561024.jpg "ω avg [between t 1 and t 2 ] = ω(t 1) + ω(t 2 ) 2")
PHY 302 K. Solutions for problem set #9. Textbook problem 7.10: For linear motion at constant acceleration a, average velocity during some time interval from t 1 to t 2 is the average of the velocities
Review questions. Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right.
Review questions Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is stationary and 70 kg ball is moving to the right. 30 kg 70 kg v (a) Is this collision elastic? (b) Find the
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
16. Rotational Dynamics
6. Rotational Dynamics A Overview In this unit we will address examples that combine both translational and rotational motion. We will find that we will need both Newton s second law and the rotational
Chapter 10. Rotation
Chapter 10 Rotation Rotation Rotational Kinematics: Angular velocity and Angular Acceleration Rotational Kinetic Energy Moment of Inertia Newton s nd Law for Rotation Applications MFMcGraw-PHY 45 Chap_10Ha-Rotation-Revised
Chap10. Rotation of a Rigid Object about a Fixed Axis
Chap10. Rotation of a Rigid Object about a Fixed Axis Level : AP Physics Teacher : Kim 10.1 Angular Displacement, Velocity, and Acceleration - A rigid object rotating about a fixed axis through O perpendicular
Lectures. Today: Rolling and Angular Momentum in ch 12. Complete angular momentum (chapter 12) and begin equilibrium (chapter 13)
Lectures Today: Rolling and Angular Momentum in ch 1 Homework 6 due Next time: Complete angular momentum (chapter 1) and begin equilibrium (chapter 13) By Monday, will post at website Sample midterm II
Chapter 10.A. Rotation of Rigid Bodies
Chapter 10.A Rotation of Rigid Bodies P. Lam 7_23_2018 Learning Goals for Chapter 10.1 Understand the equations govern rotational kinematics, and know how to apply them. Understand the physical meanings
Physics 131: Lecture 21. Today s Agenda
Physics 131: Lecture 21 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 201: Lecture 10, Pg 1 Newton s second law in rotation land Sum of the torques will equal the moment of inertia
Chapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics
Chapter 1: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational / / 1/ m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv / / 1/ I
PHY131H1F - Class 18. Torque of a quick push
Today: Today, Chapter 11: PHY131H1F - Class 18 Angular velocity and Angular acceleration vectors Torque and the Vector Cross Product Angular Momentum Conservation of Angular Momentum Gyroscopes and Precession
We define angular displacement, θ, and angular velocity, ω. What's a radian?
We define angular displacement, θ, and angular velocity, ω Units: θ = rad ω = rad/s What's a radian? Radian is the ratio between the length of an arc and its radius note: counterclockwise is + clockwise
Rotation. Rotational Variables
Rotation Rigid Bodies Rotation variables Constant angular acceleration Rotational KE Rotational Inertia Rotational Variables Rotation of a rigid body About a fixed rotation axis. Rigid Body an object that
Rotational Kinetic Energy
Lecture 17, Chapter 10: Rotational Energy and Angular Momentum 1 Rotational Kinetic Energy Consider a rigid body rotating with an angular velocity ω about an axis. Clearly every point in the rigid body
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
Lecture 7 Chapter 10,11
Lecture 7 Chapter 10,11 Rotation, Inertia, Rolling, Torque, and Angular momentum Demo Demos Summary of Concepts to Cover from chapter 10 Rotation Rotating cylinder with string wrapped around it: example
1 MR SAMPLE EXAM 3 FALL 2013
SAMPLE EXAM 3 FALL 013 1. A merry-go-round rotates from rest with an angular acceleration of 1.56 rad/s. How long does it take to rotate through the first rev? A) s B) 4 s C) 6 s D) 8 s E) 10 s. A wheel,
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
PHYSICS. Chapter 12 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 12 Lecture RANDALL D. KNIGHT Chapter 12 Rotation of a Rigid Body IN THIS CHAPTER, you will learn to understand and apply the physics
Physics 11 Fall 2012 Practice Problems 6
Physics 11 Fall 2012 Practice Problems 6 1. Two points are on a disk that is turning about a fixed axis perpendicular to the disk and through its center at increasing angular velocity. One point is on
Angular Momentum. Physics 1425 Lecture 21. Michael Fowler, UVa
Angular Momentum Physics 1425 Lecture 21 Michael Fowler, UVa A New Look for τ = Iα We ve seen how τ = Iα works for a body rotating about a fixed axis. τ = Iα is not true in general if the axis of rotation
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
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.
Physics 201, Lecture 18
q q Physics 01, Lecture 18 Rotational Dynamics Torque Exercises and Applications Rolling Motion Today s Topics Review Angular Velocity And Angular Acceleration q Angular Velocity (ω) describes how fast
ME 230: Kinematics and Dynamics Spring 2014 Section AD. Final Exam Review: Rigid Body Dynamics Practice Problem
ME 230: Kinematics and Dynamics Spring 2014 Section AD Final Exam Review: Rigid Body Dynamics Practice Problem 1. A rigid uniform flat disk of mass m, and radius R is moving in the plane towards a wall
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
jfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt
Phone : 0 903 903 7779, 98930 58881 Rotational Motion Page: 1 fo/u fopkjr Hkh# tu] ugha vkjehks dke] foifr ns[k NksM+s rqjar e/;e eu dj ';kea iq#"k flag ladyi dj] lgrs foifr vusd] ^cuk^ u NksM+s /;s; dks]
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
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
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
Work and kinetic Energy
Work and kinetic Energy Problem 66. M=4.5kg r = 0.05m I = 0.003kgm 2 Q: What is the velocity of mass m after it dropped a distance h? (No friction) h m=0.6kg mg Work and kinetic Energy Problem 66. M=4.5kg
Physics 131: Lecture 21. Today s Agenda
Physics 131: Lecture 1 Today s Agenda Rotational dynamics Torque = I Angular Momentum Physics 01: Lecture 10, Pg 1 Newton s second law in rotation land Sum of the torques will equal the moment of inertia
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
Assignment 9. to roll without slipping, how large must F be? Ans: F = R d mgsinθ.
Assignment 9 1. A heavy cylindrical container is being rolled up an incline as shown, by applying a force parallel to the incline. The static friction coefficient is µ s. The cylinder has radius R, mass
8.012 Physics I: Classical Mechanics Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE
Lecture PowerPoints. Chapter 11. Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli
Lecture PowerPoints Chapter 11 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli 2009 Pearson Education, Inc. This work is protected by United States copyright laws and is
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
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
Class XI Chapter 7- System of Particles and Rotational Motion Physics
Page 178 Question 7.1: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie
Lecture 11 - Advanced Rotational Dynamics
Lecture 11 - Advanced Rotational Dynamics A Puzzle... A moldable blob of matter of mass M and uniform density is to be situated between the planes z = 0 and z = 1 so that the moment of inertia around the
Solutions Practice Test - PHYS 211 Final Exam (New Material)
Solutions Practice Test - PHYS 11 Final Exam (New Material) 1C The question talks about gravitational forces, and so we need to use our new equation for gravitational force: F = Gm1m / r What we need to
Conservation of Angular Momentum
Physics 101 Section 3 March 3 rd : Ch. 10 Announcements: Monday s Review Posted (in Plummer s section (4) Today start Ch. 10. Next Quiz will be next week Test# (Ch. 7-9) will be at 6 PM, March 3, Lockett-6
Department of Physics
Department of Physics PHYS101-051 FINAL EXAM Test Code: 100 Tuesday, 4 January 006 in Building 54 Exam Duration: 3 hrs (from 1:30pm to 3:30pm) Name: Student Number: Section Number: Page 1 1. A car starts
Lagrangian Dynamics: Generalized Coordinates and Forces
Lecture Outline 1 2.003J/1.053J Dynamics and Control I, Spring 2007 Professor Sanjay Sarma 4/2/2007 Lecture 13 Lagrangian Dynamics: Generalized Coordinates and Forces Lecture Outline Solve one problem
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
Unit 8 Notetaking Guide Torque and Rotational Motion
Unit 8 Notetaking Guide Torque and Rotational Motion Rotational Motion Until now, we have been concerned mainly with translational motion. We discussed the kinematics and dynamics of translational motion
Chapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics
Chapter 12: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational 2 / / 1/ 2 m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv 2 /
. d. v A v B. e. none of these.
General Physics I Exam 3 - Chs. 7,8,9 - Momentum, Rotation, Equilibrium Oct. 28, 2009 Name Rec. Instr. Rec. Time For full credit, make your work clear to the grader. Show the formulas you use, the essential
PHYS 111 HOMEWORK #11
PHYS 111 HOMEWORK #11 Due date: You have a choice here. You can submit this assignment on Tuesday, December and receive a 0 % bonus, or you can submit this for normal credit on Thursday, 4 December. If
FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Monday, 14 December 2015, 6 PM to 9 PM, Field House Gym
FALL TERM EXAM, PHYS 111, INTRODUCTORY PHYSICS I Monday, 14 December 015, 6 PM to 9 PM, Field House Gym NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 13 pages. Make sure none are missing. There
Physics 218 Lecture 23
Physics 218 Lecture 23 Dr. David Toback Physics 218, Lecture XXIII 1 Checklist for Today Things due Monday Chapter 14 in WebCT Things that were due yesterday Chapter 15 problems as Recitation Prep Things