Rotational Motion. Rotational Motion. Rotational Motion

Size: px
Start display at page:

Download "Rotational Motion. Rotational Motion. Rotational Motion"

Transcription

1 I. Rotational Kinematics II. Rotational Dynamics (Netwton s Law for Rotation) III. Angular Momentum Conservation 1. Remember how Newton s Laws for translational motion were studied: 1. Kinematics (x = x 0 + v 0 t + ½ a t ). Dynamics (F = m a) 3. Momentum Conservation. Now, we repeat them again, but for rotational motion: 1. Kinematics (θ, ω, α). Dynamics (τ = I α) 3. Angular Momentum Part I Translational Motion and Today Later 1

2 Newton s s Laws for Rotation τ = Iα net nd part 1 st part 3rd part Angular Quantities Kinematical variables to describe the rotational motion: Angular position, velocity and acceleration l θ = ( rad) R θ dθ ω = lim = t 0 t dt ω ave ω dω α = lim = t 0 t dt α ave ( rad/s) ( rad/s )

3 Linear and Angular Quantities a tan a rad Vector Nature of Angular Quantities Kinematical variables to describe the rotational motion: Angular position, velocity and acceleration c.w. or c.c.w. rotation (like +x or x direction in 1D) Vector natures! l θ = R d kˆ θ ω = kˆ dt d kˆ ω α = kˆ dt ( rad) ( rad/s) ( rad/s >0 or <0 ) x z R.-H. Rule y 3

4 Example 1 ( (α = constant) (1) What is the angular speed of rotation of the Earth? 1 rotation (π rad) per 4 hours (1440 min) () An old 33 1/3 rpm record player starts from rest and reaches operating speed in.00 seconds. Through what angle did it turn in those.00 seconds? t =.00 s, ω 0 = 0, ω = 33 1/3 rpm (3) A computer hard drive rotates at 5400 rpm. What angular acceleration will get it up to speed in just 150 revolutions starting from rest? Use Eq. (3) with θ θ 0 = 150 rev. =? rad Example 1 (cont d) (4) A hard drive reaches 5400 rpm in 3.0 seconds. What was the average angular speed assuming constant angular acceleration? (5) A dentist s drill accelerates to 1800 rpm in.50 seconds. what is its angular acceleration? (6) The angular velocity changes from 47.0 rad/s to 47.0 rad/s in.00 seconds. What is the angular acceleration? 4

5 Example A grinding wheel turns at a constant angular acceleration of 60.0 rad/s from 4.0 rad/s for.00 sec. Then, a circuit breaker trips. It turns through 43 rad as it coasts to a stop at a constant angular acceleration. Find: (a) the total angle between t = 0 and the time it stopped; (b) the time it stopped; (c) the angular acceleration as it slowed down. Also sketch θ-t graph. Practice Problem 1 Problem 3: (5 points) A grinding wheel turns at a varying angular acceleration of α(t) = [30.0 rad/s 3 ] t for.00 sec. Assume the initial angular speed of 0.0 rad/s. Then, a circuit breaker trips. It turns through 400 rad as it coasts to a stop at a constant angular acceleration. a. (5 pts) Find the total angle (θ total ) between t = 0 and the time it stopped. b. (10 pts) Find the time (t total ) it stopped. Find the angular acceleration as it slowed down. c. (10 pts) Sketch θ t, ω-t, α-t graphs. 5

6 Practice Problem A solid cylinder (radius R = m and height H = 5 m) turns at a constant angular acceleration of 60.0 rad/s from 4.0 rad/s for.00 sec. Then, a circuit breaker trips. It turns through 43 rad as it coasts to a stop at a constant angular acceleration. (a) Find the total angle between t = 0 and the time it stopped. (b) Find the time it stopped. (c) Find the angular acceleration as it slowed down. 0.4H (d) Find the speed (v) of point P at t =.00 sec. (e) Sketch the motion of point P in v-t graph. Also sketch θ-t graph. ω H 1. Remember how Newton s Laws for translational motion were studied: 1. Kinematics (x = x 0 + v 0 t + ½ a t ). Dynamics (F = m a) 3. Momentum Conservation. Now, we repeat them again, but for rotational motion: 1. Kinematics (θ, ω, α). Dynamics (τ = I α) 3. Angular Momentum Part II Translational Motion and Today Later 6

7 Torque due to Gravity? τ = r F =? We assume: Center of mass (CM or cm) = Center of gravity (if uniform gravity) Torque due to Gravity? τ = r F =? mass m 7

8 Net Torque due to Gravity? One extra sphere! Do we need a new concept? No! mass m l τ net = τ rod + τ sphere Solid sphere (M, r) τ τ = F net ( R Note: sign of τ and Στ τ 1 = F 1 ( R 1 sin90 ) = (50.0N)(0.300 m) = 15.0N m = (50.0N)(0.500 m)(0.866) = 1.7N m = τ [c.c.w.] + τ [c.w.] 1 = τ [ + 1] + τ [ 1] 1 sin60 ) = [(15.0N m) (1.7N m)][c.c.w.] = 6.7N m[c.c.w.] 6.7N m[c.w.] r 1 r 8

9 Example 1 Calculate the torque on the.00-m long beam due to a 50.0 N force (top) about (a) point C (= c.m.) (b) point P Calculate the torque on the.00-m long beam due to a 60.0 N force about (a) point C (= c.m.) (b) point P Calculate the torque on the.00-m long beam due to a 50.0 N force (bottom) about (a) point C (= c.m.) (b) point P Example 1 (cont d) Calculate the net torque on the.00-m long beam about (a) point C (= c.m.) (b) point P 9

10 Ptactice Problem Determine the net torque (magnitude and direction) on the.00-m-long beam about: 50.0 N a. (15 pts) point C (the CM position); θ = 70.0 b. (10 pts) point P at one end. o τ i = ri Fi =? τ τ net = i i 60.0 N θ = 50.0 o C P θ = 33.0 o 50.0 N Ptactice Problem Determine the net torque (magnitude and direction) on the disk about pin. τ i = ri Fi =? τ τ net = i i F 1 = 50N θ 1 =40 o θ =70 o F = 5N 10

11 Newton s s Laws for Rotation τ = Iα net nd part [N m] 3rd part 1 st part [s ] Parallel-axis axis Theorem d d 1 I = I 1 + I 11

12 (a) Express the moment of inertia of the array of point objects about the y-axis in terms of m, M, X 1, X, and/or Y. Y X 1 X Newton s s Laws for Rotation τ = Iα net nd part [N m] 3 rd part [kg m ] 1 st part [s ] K rot = (1/) I ω ( K = (1/) m v ) Application? 1

13 Rolling Motion (w/o slipping) PHYSICS, R. Serway and R. Beichner, 5 th ed. Rolling Motion w/o Slipping () ω ω Faster Instantaneously rest Instantaneous axis 13

14 Example 3 What will be the speed of each of the following objects when it reaches the bottom of an incline if it starts from rest at a vertical height H and rolls without slipping? Find the speed using the conservation of mechanical energy. (i) Solid sphere (M, R 0 ) (ii) Solid cylinder (M, R 0, l) (iii) Thin hoop (M, R 0, l) Example 4 Analyze the rolling sphere in terms of forces and torques: find the magnitudes of the velocity v and the friction force F fr. 1. F.B.D.? Rolling Motion (w/o slipping). Is F fr static or kinetic friction? Static Friction No work No energy loss K+U=constant P is: (a) the point of contact with the ground; (b) instantaneously rest relative to the ground. Thus: The motion of the wheel is a pure rotation about the instantaneous axis through P at the instant. 14

15 Example 5 A sting is wrapped around a uniform solid cylinder of mass M (= kg) and radius R (= 0.00 m), and the cylinder starts falling from rest. Draw the freebody diagram for the cylinder while it descends. A l s o f i n d ( a ) i t s acceleration, (b) the tension in the string, and (c) the speed after the cylinder has descended h = m. Example 5 - Challenge A sting is wrapped around a hollow cylinder of mass M (= kg), inner radius R 1 (= m), outer radius R (= 0.00 m). The cylinder starts falling from rest. (a) Draw the free-body diagram for the cylinder while it descends. Also find: (b) its acceleration; (c) the tension in the string; (d) the speed after the cylinder has descended h = m. 15

Chap. 10: Rotational Motion

Chap. 10: Rotational Motion Chap. 10: Rotational Motion I. Rotational Kinematics II. Rotational Dynamics - Newton s Law for Rotation III. Angular Momentum Conservation (Chap. 10) 1 Newton s Laws for Rotation n e t I 3 rd part [N

More information

General Definition of Torque, final. Lever Arm. General Definition of Torque 7/29/2010. Units of Chapter 10

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

More information

31 ROTATIONAL KINEMATICS

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

More information

Rotational Motion and Torque

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

More information

III. Angular Momentum Conservation (Chap. 10) Rotation. We repeat Chap. 2-8 with rotatiing objects. Eqs. of motion. Energy.

III. Angular Momentum Conservation (Chap. 10) Rotation. We repeat Chap. 2-8 with rotatiing objects. Eqs. of motion. Energy. Chap. 10: Rotational Motion I. Rotational Kinematics II. Rotational Dynamics - Newton s Law for Rotation III. Angular Momentum Conservation (Chap. 10) 1 Toward Exam 3 Eqs. of motion o To study angular

More information

1 MR SAMPLE EXAM 3 FALL 2013

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,

More information

Rotational Kinematics and Dynamics. UCVTS AIT Physics

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,

More information

FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Thursday, 11 December 2014, 6 PM to 9 PM, Field House Gym

FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Thursday, 11 December 2014, 6 PM to 9 PM, Field House Gym FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Thursday, 11 December 2014, 6 PM to 9 PM, Field House Gym NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 13 pages. Make sure none are missing 2.

More information

Circular Motion, Pt 2: Angular Dynamics. Mr. Velazquez AP/Honors Physics

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

More information

Chapter 10. Rotation of a Rigid Object about a Fixed Axis

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

More information

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 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

More information

Lecture PowerPoints. Chapter 10 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli

Lecture PowerPoints. Chapter 10 Physics for Scientists and Engineers, with Modern Physics, 4 th edition Giancoli Lecture PowerPoints Chapter 10 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

More information

Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/1

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

More information

Chapter 8 Lecture Notes

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

More information

Chapter 8- Rotational Kinematics Angular Variables Kinematic Equations

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

More information

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 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

More information

CHAPTER 8: ROTATIONAL OF RIGID BODY PHYSICS. 1. Define Torque

CHAPTER 8: ROTATIONAL OF RIGID BODY PHYSICS. 1. Define Torque 7 1. Define Torque 2. State the conditions for equilibrium of rigid body (Hint: 2 conditions) 3. Define angular displacement 4. Define average angular velocity 5. Define instantaneous angular velocity

More information

ΣF = ma Στ = Iα ½mv 2 ½Iω 2. mv Iω

ΣF = ma Στ = Iα ½mv 2 ½Iω 2. mv Iω Thur Oct 22 Assign 9 Friday Today: Torques Angular Momentum x θ v ω a α F τ m I Roll without slipping: x = r Δθ v LINEAR = r ω a LINEAR = r α ΣF = ma Στ = Iα ½mv 2 ½Iω 2 I POINT = MR 2 I HOOP = MR 2 I

More information

Physics 4A Solutions to Chapter 10 Homework

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

More information

Test 7 wersja angielska

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

More information

= o + t = ot + ½ t 2 = o + 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

More information

Moment of Inertia & Newton s Laws for Translation & Rotation

Moment of Inertia & Newton s Laws for Translation & Rotation Moment of Inertia & Newton s Laws for Translation & Rotation In this training set, you will apply Newton s 2 nd Law for rotational motion: Στ = Σr i F i = Iα I is the moment of inertia of an object: I

More information

Chapter 9-10 Test Review

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

More information

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. 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

More information

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. 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

More information

We define angular displacement, θ, and angular velocity, ω. What's a radian?

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

More information

Physics 101 Lecture 11 Torque

Physics 101 Lecture 11 Torque Physics 101 Lecture 11 Torque Dr. Ali ÖVGÜN EMU Physics Department www.aovgun.com Force vs. Torque q Forces cause accelerations q What cause angular accelerations? q A door is free to rotate about an axis

More information

Physics 131: Lecture 21. Today s Agenda

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

More information

CHAPTER 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WEN-BIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY

CHAPTER 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WEN-BIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY CHAPTER 10 ROTATION OF A RIGID OBJECT ABOUT A FIXED AXIS WEN-BIN JIAN ( 簡紋濱 ) DEPARTMENT OF ELECTROPHYSICS NATIONAL CHIAO TUNG UNIVERSITY OUTLINE 1. Angular Position, Velocity, and Acceleration 2. Rotational

More information

Description: Using conservation of energy, find the final velocity of a "yo yo" as it unwinds under the influence of gravity.

Description: Using conservation of energy, find the final velocity of a yo yo as it unwinds under the influence of gravity. Chapter 10 [ Edit ] Overview Summary View Diagnostics View Print View with Answers Chapter 10 Due: 11:59pm on Sunday, November 6, 2016 To understand how points are awarded, read the Grading Policy for

More information

Two-Dimensional Rotational Kinematics

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

More information

16. Rotational Dynamics

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

More information

Big Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular

Big Idea 4: Interactions between systems can result in changes in those systems. Essential Knowledge 4.D.1: Torque, angular velocity, angular 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

More information

Chapter 8: Momentum, Impulse, & Collisions. Newton s second law in terms of momentum:

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.)

More information

Name: Date: Period: AP Physics C Rotational Motion HO19

Name: Date: Period: AP Physics C Rotational Motion HO19 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

More information

Rotational Dynamics continued

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

More information

Rotation. Rotational Variables

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

More information

Rotation. PHYS 101 Previous Exam Problems CHAPTER

Rotation. PHYS 101 Previous Exam Problems CHAPTER 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

More information

Physics 101 Lecture 12 Equilibrium and Angular Momentum

Physics 101 Lecture 12 Equilibrium and Angular Momentum Physics 101 Lecture 1 Equilibrium and Angular Momentum Ali ÖVGÜN EMU Physics Department www.aovgun.com Static Equilibrium q Equilibrium and static equilibrium q Static equilibrium conditions n Net external

More information

Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium

Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium Physics 101: Lecture 15 Torque, F=ma for rotation, and Equilibrium Strike (Day 10) Prelectures, checkpoints, lectures continue with no change. Take-home quizzes this week. See Elaine Schulte s email. HW

More information

Webreview Torque and Rotation Practice Test

Webreview Torque and Rotation Practice Test 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

More information

Rolling without slipping Angular Momentum Conservation of Angular Momentum. Physics 201: Lecture 19, Pg 1

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

More information

Suggested Problems. Chapter 1

Suggested Problems. Chapter 1 Suggested Problems Ch1: 49, 51, 86, 89, 93, 95, 96, 102. Ch2: 9, 18, 20, 44, 51, 74, 75, 93. Ch3: 4, 14, 46, 54, 56, 75, 91, 80, 82, 83. Ch4: 15, 59, 60, 62. Ch5: 14, 52, 54, 65, 67, 83, 87, 88, 91, 93,

More information

Chapter 10 Practice Test

Chapter 10 Practice Test Chapter 10 Practice Test 1. At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of 0.40 rad/s 2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. What

More information

Torque/Rotational Energy Mock Exam. Instructions: (105 points) Answer the following questions. SHOW ALL OF YOUR WORK.

Torque/Rotational Energy Mock Exam. Instructions: (105 points) Answer the following questions. SHOW ALL OF YOUR WORK. 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

More information

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm.

6. Find the net torque on the wheel in Figure about the axle through O if a = 10.0 cm and b = 25.0 cm. 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

More information

PLANAR KINETICS OF A RIGID BODY: WORK AND ENERGY Today s Objectives: Students will be able to: 1. Define the various ways a force and couple do work.

PLANAR KINETICS OF A RIGID BODY: WORK AND ENERGY Today s Objectives: Students will be able to: 1. Define the various ways a force and couple do work. PLANAR KINETICS OF A RIGID BODY: WORK AND ENERGY Today s Objectives: Students will be able to: 1. Define the various ways a force and couple do work. In-Class Activities: 2. Apply the principle of work

More information

Physics 131: Lecture 21. Today s Agenda

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

More information

Plane Motion of Rigid Bodies: Forces and Accelerations

Plane Motion of Rigid Bodies: Forces and Accelerations Plane Motion of Rigid Bodies: Forces and Accelerations Reference: Beer, Ferdinand P. et al, Vector Mechanics for Engineers : Dynamics, 8 th Edition, Mc GrawHill Hibbeler R.C., Engineering Mechanics: Dynamics,

More information

Chapter 10. Rotation

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

More information

Welcome back to Physics 211

Welcome back to Physics 211 Welcome back to Physics 211 Today s agenda: Moment of Inertia Angular momentum 13-2 1 Current assignments Prelecture due Tuesday after Thanksgiving HW#13 due next Wednesday, 11/24 Turn in written assignment

More information

Rotational Kinematics

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

More information

PHY131H1S - Class 20. Pre-class reading quiz on Chapter 12

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

More information

PLANAR KINETIC EQUATIONS OF MOTION (Section 17.2)

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

More information

Translational vs Rotational. m x. Connection Δ = = = = = = Δ = = = = = = Δ =Δ = = = = = 2 / 1/2. Work

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

More information

Unit 8 Notetaking Guide Torque and Rotational Motion

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

More information

Do not fill out the information below until instructed to do so! Name: Signature: Student ID: Section Number:

Do not fill out the information below until instructed to do so! Name: Signature: Student ID:   Section Number: Do not fill out the information below until instructed to do so! Name: Signature: Student ID: E-mail: Section Number: Formulae are provided on the last page. You may NOT use any other formula sheet. You

More information

Forces of Rolling. 1) Ifobjectisrollingwith a com =0 (i.e.no netforces), then v com =ωr = constant (smooth roll)

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/

More information

Chap10. Rotation of a Rigid Object about a Fixed Axis

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

More information

Review for 3 rd Midterm

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

More information

Dynamics of Rotational Motion

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

More information

Torque rotational force which causes a change in rotational motion. This force is defined by linear force multiplied by a radius.

Torque rotational force which causes a change in rotational motion. This force is defined by linear force multiplied by a radius. Warm up A remote-controlled car's wheel accelerates at 22.4 rad/s 2. If the wheel begins with an angular speed of 10.8 rad/s, what is the wheel's angular speed after exactly three full turns? AP Physics

More information

Q1. For a completely inelastic two-body collision the kinetic energy of the objects after the collision is the same as:

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

More information

11-2 A General Method, and Rolling without Slipping

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

More information

Physics 207: Lecture 24. Announcements. No labs next week, May 2 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here.

Physics 207: Lecture 24. Announcements. No labs next week, May 2 5 Exam 3 review session: Wed, May 4 from 8:00 9:30 pm; here. 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

More information

Chapter 9 [ Edit ] Ladybugs on a Rotating Disk. v = ωr, where r is the distance between the object and the axis of rotation. Chapter 9. Part A.

Chapter 9 [ Edit ] Ladybugs on a Rotating Disk. v = ωr, where r is the distance between the object and the axis of rotation. Chapter 9. Part A. Chapter 9 [ Edit ] Chapter 9 Overview Summary View Diagnostics View Print View with Answers Due: 11:59pm on Sunday, October 30, 2016 To understand how points are awarded, read the Grading Policy for this

More information

End-of-Chapter Exercises

End-of-Chapter Exercises 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

More information

PHYSICS 149: Lecture 21

PHYSICS 149: Lecture 21 PHYSICS 149: Lecture 21 Chapter 8: Torque and Angular Momentum 8.2 Torque 8.4 Equilibrium Revisited 8.8 Angular Momentum Lecture 21 Purdue University, Physics 149 1 Midterm Exam 2 Wednesday, April 6, 6:30

More information

Physics for Scientist and Engineers third edition Rotational Motion About a Fixed Axis Problems

Physics for Scientist and Engineers third edition Rotational Motion About a Fixed Axis Problems 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

More information

Rotational Motion What is the difference between translational and rotational motion? Translational motion.

Rotational Motion What is the difference between translational and rotational motion? Translational motion. Rotational Motion 1 1. What is the difference between translational and rotational motion? Translational motion Rotational motion 2. What is a rigid object? 3. What is rotational motion? 4. Identify and

More information

PHYSICS 220. Lecture 15. Textbook Sections Lecture 15 Purdue University, Physics 220 1

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

More information

Rotational Kinetic Energy

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

More information

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

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

More information

Physics 111. Lecture 23 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, Kinetic Energy of Rolling Object

Physics 111. Lecture 23 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, Kinetic Energy of Rolling Object Physics 111 Lecture 3 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, 009 Lecture 3 1/4 Kinetic Energy of Rolling Object Total kinetic energy of a rolling object is the sum of

More information

AP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems

AP Physics C: Rotation II. (Torque and Rotational Dynamics, Rolling Motion) Problems AP Physics C: Rotation II (Torque and Rotational Dynamics, Rolling Motion) Problems 1980M3. A billiard ball has mass M, radius R, and moment of inertia about the center of mass I c = 2 MR²/5 The ball is

More information

CEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5

CEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5 1 / 36 CEE 271: Applied Mechanics II, Dynamics Lecture 25: Ch.17, Sec.4-5 Prof. Albert S. Kim Civil and Environmental Engineering, University of Hawaii at Manoa Date: 2 / 36 EQUATIONS OF MOTION: ROTATION

More information

Rotation. Kinematics Rigid Bodies Kinetic Energy. Torque Rolling. featuring moments of Inertia

Rotation. Kinematics Rigid Bodies Kinetic Energy. Torque Rolling. featuring moments of Inertia 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

More information

. d. v A v B. e. none of these.

. 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

More information

Physics 2210 Homework 18 Spring 2015

Physics 2210 Homework 18 Spring 2015 Physics 2210 Homework 18 Spring 2015 Charles Jui April 12, 2015 IE Sphere Incline Wording A solid sphere of uniform density starts from rest and rolls without slipping down an inclined plane with angle

More information

EQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body

EQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body EQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body undergoing general plane motion. APPLICATIONS As the soil

More information

PHYS 111 HOMEWORK #11

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

More information

Chapter 8 continued. Rotational Dynamics

Chapter 8 continued. Rotational Dynamics Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = rφ = Frφ Fr = τ (torque) = τφ r φ s F to x θ = 0 DEFINITION OF

More information

Phys101 Lectures 19, 20 Rotational Motion

Phys101 Lectures 19, 20 Rotational Motion 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

More information

Relating Linear and Angular Kinematics. a rad = v 2 /r = rω 2

Relating Linear and Angular Kinematics. a rad = v 2 /r = rω 2 PH2213 : Advanced Examples from Chapter 10 : Rotational Motion NOTE: these are somewhat advanced examples of how we can apply the methods from this chapter, so are beyond what will be on the final exam

More information

Rotation review packet. Name:

Rotation review packet. Name: Rotation review packet. Name:. A pulley of mass m 1 =M and radius R is mounted on frictionless bearings about a fixed axis through O. A block of equal mass m =M, suspended by a cord wrapped around the

More information

AP Physics 1 Rotational Motion Practice Test

AP Physics 1 Rotational Motion Practice Test AP Physics 1 Rotational Motion Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A spinning ice skater on extremely smooth ice is able

More information

Midterm 3 Review (Ch 9-14)

Midterm 3 Review (Ch 9-14) Midterm 3 Review (Ch 9-14) PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Copyright 2008 Pearson Education Inc., publishing as Pearson

More information

Torque. Introduction. Torque. PHY torque - J. Hedberg

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

More information

Lecture 6 Physics 106 Spring 2006

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/

More information

Phys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw

Phys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw Coordinator: Dr. M. Al-Kuhaili Thursday, August 2, 218 Page: 1 Q1. A car, of mass 23 kg, reaches a speed of 29. m/s in 6.1 s starting from rest. What is the average power used by the engine during the

More information

Lecture 11 - Advanced Rotational Dynamics

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

More information

Chapter 6, Problem 18. Agenda. Rotational Inertia. Rotational Inertia. Calculating Moment of Inertia. Example: Hoop vs.

Chapter 6, Problem 18. Agenda. Rotational Inertia. Rotational Inertia. Calculating Moment of Inertia. Example: Hoop vs. Agenda Today: Homework quiz, moment of inertia and torque Thursday: Statics problems revisited, rolling motion Reading: Start Chapter 8 in the reading Have to cancel office hours today: will have extra

More information

Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS

Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS Accelerated Physics Rotational Dynamics Problem Set Page 1 of 5 Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS Directions: Show all work on a separate piece of paper. Box your final answer. Don t forget

More information

Chapter 8. Rotational Equilibrium and Rotational Dynamics

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

More information

Centripetal acceleration ac = to2r Kinetic energy of rotation KE, = \lto2. Moment of inertia. / = mr2 Newton's second law for rotational motion t = la

Centripetal acceleration ac = to2r Kinetic energy of rotation KE, = \lto2. Moment of inertia. / = mr2 Newton's second law for rotational motion t = la The Language of Physics Angular displacement The angle that a body rotates through while in rotational motion (p. 241). Angular velocity The change in the angular displacement of a rotating body about

More information

are (0 cm, 10 cm), (10 cm, 10 cm), and (10 cm, 0 cm), respectively. Solve: The coordinates of the center of mass are = = = (200 g g g)

are (0 cm, 10 cm), (10 cm, 10 cm), and (10 cm, 0 cm), respectively. Solve: The coordinates of the center of mass are = = = (200 g g g) Rotational Motion Problems Solutions.. Model: A spinning skater, whose arms are outstretched, is a rigid rotating body. Solve: The speed v rω, where r 40 / 0.70 m. Also, 80 rpm (80) π/60 rad/s 6 π rad/s.

More information

Kinematics (special case) Dynamics gravity, tension, elastic, normal, friction. Energy: kinetic, potential gravity, spring + work (friction)

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

More information

Rolling, Torque, Angular Momentum

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

More information

TutorBreeze.com 7. ROTATIONAL MOTION. 3. If the angular velocity of a spinning body points out of the page, then describe how is the body spinning?

TutorBreeze.com 7. ROTATIONAL MOTION. 3. If the angular velocity of a spinning body points out of the page, then describe how is the body spinning? 1. rpm is about rad/s. 7. ROTATIONAL MOTION 2. A wheel rotates with constant angular acceleration of π rad/s 2. During the time interval from t 1 to t 2, its angular displacement is π rad. At time t 2

More information

Angular Displacement. θ i. 1rev = 360 = 2π rads. = "angular displacement" Δθ = θ f. π = circumference. diameter

Angular Displacement. θ i. 1rev = 360 = 2π rads. = angular displacement Δθ = θ f. π = circumference. diameter Rotational Motion Angular Displacement π = circumference diameter π = circumference 2 radius circumference = 2πr Arc length s = rθ, (where θ in radians) θ 1rev = 360 = 2π rads Δθ = θ f θ i = "angular displacement"

More information