2 Rotational Coordinates Ridged objects require six numbers to describe their position and orientation: 3 coordinates 3 axes of rotation
3 Rotational Coordinates Use an angle θ to describe rotations about a single fixed axis. Always measure θ in radians. θ f Δθ θ 0
4 Rotational Coordinates The angle θ takes the place of a translational coordinate, x, y, or z. We define the change in Δθ as: Δθ = θ f θ 0
5 Rotational Velocity Just like we defined velocity for translational motion, we can define velocity for rotations as well. ω avg = Δθ Δt Instantaneous angular velocity is defined as: ω = dθ dt
6 Rotational Acceleration We also define rotational acceleration as: α avg = Δω Δt And instantaneous angular acceleration as: α = dω dt = d2 θ dt 2
7 Rotational-Translational Analog v avg = Δx Δt a avg = Δv Δt ω avg = Δθ Δt α avg = Δω Δt The definitions of angular velocity and acceleration are analogous to the definitions for translational velocity and acceleration.
8 Rotational Kinematics Just like with translational motion, we can relate Δθ, ω, and α. Δθ = ω avg Δt Δω = α avg Δt For constant angular acceleration ω avg = 1 ω ω f Δθ = 1 α Δt 2 + ω 2 0 Δt ω 2 f = ω α Δθ
9 Rotational-Translational Analog v avg = Δx Δt a = Δv Δt v avg = 1 2 v 0 + v f ω avg = Δθ Δt α = Δω Δt ω avg = 1 2 ω 0 + ω f Δx = 1 2 a Δt 2 + v 0 Δt Δθ = 1 2 α Δt 2 v f 2 = v a Δx ω f 2 = ω α Δθ The rotational kinematic equations are analogous to the translational kinematic equations.
10 Rotational-Translational Analog Δx = t 0 t fv t dt Δθ = t 0 t fω t dt Δv = t 0 t fa t dt Δω = t 0 t fα t dt The same analogs extend to non-constant acceleration problems as well.
11 Rotational-Translational Analogy The rotational and translational equations are analogous. Replace: Δx Δθ v ω a α
12 Right Hand Rule #1 Like their translational counterparts Δθ, ω, and α are vectors. How do we describe the direction of ω? Use the Right Hand Rule
13 Right Hand Rule #1 Right Hand Rule #1: Curl the fingers on your right hand in the direction of the rotation, your thumb will point in the direction of Δ θ and ω. ω
14 Direction of Angular Acceleration The direction of α is given by: In general: α = ω f ω 0 Δt If ω is increasing, α points in the same direction as ω. If ω is decreasing, α points in the opposite direction from ω.
15 Rolling Without Slipping Δx
16 Rolling Without Slipping Whenever a wheel or pulley rolls without slipping: Δx = r Δθ v = r ω a = r α
17 Translations From Rotation s =? What about the velocity and acceleration of a point on a rotating wheel?
18 Translations From Rotations The displacement and speed of a point on a spinning object is found by: s = r Δθ v = r ω Note that this does not work for acceleration: a r α
19 Rotational Accelerations Recall that it is the component of the acceleration that points parallel to v that is responsible for changing an object s speed. Therefore, a t = r α Where a t is the component of a that points tangent to the circular path.
20 Rotational Accelerations When an object travels around a circular path the acceleration is broken into two parts: Tangent Causes the change in the object s speed a a c a t Centripetal Causes the change in the object s direction
21 Acceleration Uniform Circular Motion Uniform Circular Motion ω is constant Although speed is constant, acceleration is non-zero The acceleration responsible for uniform circular motion is called centripetal acceleration We can calculate a c by relating Δ v to Δt
22 v f r f v 0 r 0
23 v f Δ v v 0 r f Δθ r 0 v 0
24 Centripetal Acceleration When an object travels with uniform circular motion, the acceleration always points towards the center of the circular path with: a c = v2 r = r ω2
25 Centripetal Acceleration - Example A centrifuge starts from rest and experiences a constant rotational acceleration of 4 rad.. The average radius s 2 of the arm of the centrifuge is r = 5 cm. What is the acceleration of the centrifuge after completing one quarter of a rotation?
26 a c = 6250 g = m s 2 v =? r = 0.05 m ω =?
27 Centripetal Acceleration - Example A circular track has a radius of 500 m. When the race starts, the diver hits the gas peddle, causing the car s speed to increase at a rate of 6 m s 2. What is the magnitude of the car s acceleration after 10 s have passed?
28 a c = 6250 g = m s 2 v =? r = 0.05 m ω =?
29 Centripetal Acceleration - Example A car drives around a level turn. The tires have a coefficient of friction of μ s = 0.8, and the turn has a radius of 900 m. How fast can the car go around the turn without sliding?
30 N r v =? F c =? F c W
31 Centripetal Acceleration - Example A car drives around an banked turn with a radius of 900 m. The turn is designed so that a car traveling 10 m/s will be able go around the turn even when the coefficient of friction is reduced to μ s = 0. What angle is the turn banked at?
32 N y N θ N x r v =? F c θ W
33 Newton s Law of Universal Gravity Every particle exerts an attractive force all other particles The force is given by: F G = Gm 1m 2 r 2 G is the universal gravitational constant: G = N m2 kg 2
34 Newton s Law of Universal Gravity F G = Gm 1m 2 r 2 Note that r, is the distance between the centers of the two masses Therefore, when standing on the surface of the Earth: r = R E + h R E
35 Orbit Any force can supply the centripetal force required to keep an object in uniform circular motion. When a satellite obits the Earth, the centripetal force is supplied by the gravitational force. F g
36 Orbit An important problem in orbital motion is determining how fast a satellite must move to stay in orbit. Suppose a satellite is a distance r from the center of the Earth, how fast must it move?
37 Kepler s Third Law of Planetary Motion Kepler s Third Law relates the period T to the radius of the orbit R
38 Kepler s Third Law of Planetary Motion Kepler s Third Law of Planetary Motion Says: T 2 R 3 = const.
39 Cross-Product To discuss the effect that a force has on a rotating object, we need to introduce a new type of vector operation: The Cross-Product
40 Cross-Product The Cross-Product, also known as a vector product, is a product between two vectors: A B = C
41 Cross-Product The Cross-Product A B = C is defined as: C = A y B z A z B y + A z B x A x B z i j + A x B y A y B x k
42 Cross-Product An easy way to remember the formula for A B is: i j k A B = det A x A y A z B x B y B z
43 Cross-Product In general, the magnitude of the crossproduct is given by: A B = A B sin θ How do we find the direction of A B?
44 Right Hand Rule #2 A B A B
45 Torque Toque is denoted by the Greek letter tau, τ Torque is the rotational analog of a force The torque describes the tendency for a force to cause rotational acceleration.
46 Torque F Applying a force further from the pivot increases the torque. The distance between the force and the axis of rotation is called the lever arm.
47 Torque F r r F F t Only the component of the force that is perpendicular to the lever arm generates a torque.
48 Torque In general: τ = F t r = F r sin θ
49 Torque Clearly τ is a cross-product between F and r. But is it: F r or r F We want τ to point in the direction of α.
50 Torque In general: τ = r F
51 Torque - Example A rope is wrapped around a circular disk with a radius of 0.1 m. A 50 N force is applied to the rope as shown in the figure. What is the torque generated by the tension in the rope? 100 N R
52 Torque - Example Now the force is applied at an angle. What is the torque generated by the tension in the rope? R N
53 Rotational Dynamics What does torque tell us? Consider a force applied to a single point mass: F = m a To find the effect of torque, cross both sides with r: r F = m r a
54 In general: Rotational Dynamics τ = m r 2 α I Where I describes the rotational inertia of the point mass. I is called the moment of inertia.
55 Rotational-Translational Analog F = m a τ = I α Translational to Rotational: F τ a α m I
56 Moment of Inertia Formulas for the moment of inertia of various shapes can be found in tables like this.
57 Torque - Example A box of mass m hangs from a massless string which winds around a circular disk of mass M and radius R. What is the acceleration of the mass?
58 R M m
59 Torque - Example Tension can not be the same M on opposite sides of a massive pulley. Since, τ = T 1 T 2 R = I α T 1 T 2
60 Torque - Example R Calculate the acceleration of M an Atwood Machine with for masses m 1 > m 2 and a pulley of mass M and radius R. m 1 m 2
61 R M m 1 m 2
62 Moment of Inertia Moment of Inertia is rotational inertia For a collection of rigidly attached masses: I = n m n r n 2
63 Moment of Inertia For a solid continuous object, the moment of inertia is calculated by: I = r 2 dm Where dm is the mass of an infinitesimal piece of the object.
64 Moment of Inertia I = r 2 dm For a: Rod dm = λ dx; λ = mass length Disk dm = σ da; σ = mass area Volume dm = ρ dv; ρ = mass volume
65 Moment of Inertia Calculate the moment of inertia of a metal rod of length L and mass M rotated about one end.
66 x = 0 M L x = L
67 Moment of Inertia Calculate the moment of inertia of a metal rod of length L and mass M rotated about its center.
68 M x = L 2 L x = + L 2
69 Parallel Axis Theorem The moment of inertia of an object depends on the location of axis of rotation. The moment of inertia about any axis can be related to the moment of inertia about the center of mass using the parallel axis theorem.
70 Parallel Axis Theorem The Parallel Axis Theorem states: The moment of inertia of an object of mass M rotated about an axis a distance R from the center of mass, is given by: I = I cm + M R 2
71 Parallel Axis Theorem M L 2 L I I= cm I= 1 cm + M L L
Circular Motion Uniform Circular Motion Uniform Circular Motion Traveling with a constant speed in a circular path Even though the speed is constant, the acceleration is non-zero The acceleration responsible
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
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
Rotation Kinematics Rigid Bodies Kinetic Energy featuring moments of Inertia Torque Rolling Angular Motion We think about rotation in the same basic way we do about linear motion How far does it go? How
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
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
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
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
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
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
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
Phys101 Lectures 19, 20 Rotational Motion Key points: Angular and Linear Quantities Rotational Dynamics; Torque and Moment of Inertia Rotational Kinetic Energy Ref: 10-1,2,3,4,5,6,8,9. Page 1 Angular Quantities
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
PHYSICS 1, FALL 010 EXAM 1 Solutions WEDNESDAY, SEPTEMBER 9, 010 Note: The unit vectors in the +x, +y, and +z directions of a right-handed Cartesian coordinate system are î, ĵ, and ˆk, respectively. In
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,
Unit 7: Rotational Motion (angular kinematics, dynamics, momentum & energy) Name: Big Idea 3: The interactions of an object with other objects can be described by forces. Essential Knowledge 3.F.1: Only
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
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
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
APC PHYSICS CHAPTER 11 Mr. Holl Rotation Student Notes 11-1 Translation and Rotation All of the motion we have studied to this point was linear or translational. Rotational motion is the study of spinning
PHYS 101 Previous Exam Problems CHAPTER 10 Rotation Rotational kinematics Rotational inertia (moment of inertia) Kinetic energy Torque Newton s 2 nd law Work, power & energy conservation 1. Assume that
1301W.600 Lecture 16 November 6, 2017 You are Cordially Invited to the Physics Open House Friday, November 17 th, 2017 4:30-8:00 PM Tate Hall, Room B20 Time to apply for a major? Consider Physics!! Program
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
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
Chapter 7 Rotational Motion and The Law of Gravity 1 The Radian The radian is a unit of angular measure The radian can be defined as the arc length s along a circle divided by the radius r s θ = r 2 More
MECHANICAL PRINCIPLES OUTCOME 3 CENTRIPETAL ACCELERATION AND CENTRIPETAL FORCE TUTORIAL 1 CENTRIFUGAL FORCE Centripetal acceleration and force: derivation of expressions for centripetal acceleration and
Rotational Kinematics 1 Linear Motion Rotational Motion all variables considered positive if motion in counterclockwise direction displacement velocity acceleration angular displacement (Δθ) angular velocity
Physics 07: Lecture 4 Announcements No labs next week, May 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here Today s Agenda ecap: otational dynamics and torque Work and energy with example Many
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
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
8.01x Classical Mechanics, Fall 2016 Massachusetts Institute of Technology Problem Set 10 1. Moment of Inertia: Disc and Washer (a) A thin uniform disc of mass M and radius R is mounted on an axis passing
Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1 1. A 50-kg boy and a 40-kg girl sit on opposite ends of a 3-meter see-saw. How far from the girl should the fulcrum be placed in order for the
End-of-Chapter Exercises Exercises 1 12 are conceptual questions that are designed to see if you have understood the main concepts of the chapter. 1. Figure 11.21 shows four different cases involving a
Physics 8 Friday, November 4, 2011 Please turn in Homework 7. I will hand out solutions once everyone is here. The handout also includes HW8 and a page or two of updates to the equation sheet needed to
Name (please print): UW ID# score last first Question I. (20 pts) Projectile motion A ball of mass 0.3 kg is thrown at an angle of 30 o above the horizontal. Ignore air resistance. It hits the ground 100
1.) A wheel turns with constant acceleration 0.450 rad/s 2. (9-9) Rotational Motion H19 How much time does it take to reach an angular velocity of 8.00 rad/s, starting from rest? Through how many revolutions
Physics 8 Monday, October 28, 2013 Turn in HW8 today. I ll make them less difficult in the future! Rotation is a hard topic. And these were hard problems. HW9 (due Friday) is 7 conceptual + 8 calculation
Please do not write on test. ID A Webreview - 8.2 Torque and Rotation Practice Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A 0.30-m-radius automobile
Uniform Circular Motion Motion in a circle at constant angular speed. ω: angular velocity (rad/s) Rotation Angle The rotation angle is the ratio of arc length to radius of curvature. For a given angle,
A dentist s drill starts from rest. After 3.20 s of constant angular acceleration, it turns at a rate of 2.51 10 4 rev/min. (a) Find the drill s angular acceleration. (b) Determine the angle (in radians)
Rotational Motion and the Law of Gravity 1 Linear motion is described by position, velocity, and acceleration. Circular motion repeats itself in circles around the axis of rotation Ex. Planets in orbit,
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
PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
Physics 2211 ABC Quiz #3 Solutions Spring 2017 I. (16 points) A block of mass m b is suspended vertically on a ideal cord that then passes through a frictionless hole and is attached to a sphere of mass
PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
Chapter 10 Rotational Kinematics and Energy 10-1 Angular Position, Velocity, and Acceleration 10-1 Angular Position, Velocity, and Acceleration Degrees and revolutions: 10-1 Angular Position, Velocity,
Worksheet for Exploration 10.1: Constant Angular Velocity Equation By now you have seen the equation: θ = θ 0 + ω 0 *t. Perhaps you have even derived it for yourself. But what does it really mean for the
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
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
Physics Chapter 8 Rotational Motion Circular Motion Tangential Speed The linear speed of something moving along a circular path. Symbol is the usual v and units are m/s Rotational Speed Number of revolutions
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
1. During a certain period of time, the angular position of a swinging door is described by θ = 5.00 + 10.0t + 2.00t 2, where θ is in radians and t is in seconds. Determine the angular position, angular
Chapter 17 Two Dimensional Rotational Dynamics 17.1 Introduction... 1 17.2 Vector Product (Cross Product)... 2 17.2.1 Right-hand Rule for the Direction of Vector Product... 3 17.2.2 Properties of the Vector
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
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
!! www.clutchprep.com ROTATIONAL POSITION & DISPLACEMENT Rotational Motion is motion around a point, that is, in a path. - The rotational equivalent of linear POSITION ( ) is Rotational/Angular position
Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class
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
PHYS 101 second major Exam Term 102 (Zero Version) Q1. A 15.0-kg block is pulled over a rough, horizontal surface by a constant force of 70.0 N acting at an angle of 20.0 above the horizontal. The block
Chapter 8 Rotational Motion Chapter 8 Rotational Motion In this chapter you will: Learn how to describe and measure rotational motion. Learn how torque changes rotational velocity. Explore factors that
FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Saturday, 14 December 2013, 1PM to 4 PM, AT 1003 NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 14 pages. Make sure none are missing 2. There is
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
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
AP Physics C Spring, 2017 Torque/Rotational Energy Mock Exam Name: Answer Key Mr. Leonard Instructions: (105 points) Answer the following questions. SHOW ALL OF YOUR WORK. (22 pts ) 1. Two masses are attached
Welcome back to Physics 211 Today s agenda: Circular Motion 04-2 1 Exam 1: Next Tuesday (9/23/14) In Stolkin (here!) at the usual lecture time Material covered: Textbook chapters 1 4.3 s up through 9/16
Name: Date: _ Practice Test 3 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A wheel rotates about a fixed axis with an initial angular velocity of 20
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
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
Solution to phys101-t112-final Exam Q1. An 800-N man stands halfway up a 5.0-m long ladder of negligible weight. The base of the ladder is.0m from the wall as shown in Figure 1. Assuming that the wall-ladder
AP practice ch 7-8 Multiple Choice 1. A spool of thread has an average radius of 1.00 cm. If the spool contains 62.8 m of thread, how many turns of thread are on the spool? "Average radius" allows us to
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:
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
PHYS 2211 A, B, & C Final Exam Formulæ & Constants Spring 2017 Unless otherwise directed, drag is to be neglected and all problems take place on Earth, use the gravitational definition of weight, and all
A particular bird s eye can just distinguish objects that subtend an angle no smaller than about 3 E -4 rad, A) How many degrees is this B) How small an object can the bird just distinguish when flying
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
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
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
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
Physics 8 Friday, October 20, 2017 HW06 is due Monday (instead of today), since we still have some rotation ideas to cover in class. Pick up the HW07 handout (due next Friday). It is mainly rotation, plus