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

Save this PDF as:

Size: px
Start display at page:

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

1 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 on Thursday morning (9-11:30) Chapter 6, Problem 18 A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm. a. What is the (linear) speed of the block? b. What is the tension in the string? Rotational Inertia Rotational inertia depends on Total mass of the object Distribution of the mass relative to axis Farther the mass is from the axis of rotation, the larger the rotational inertia. Rotational inertia ~ (mass) x (axis_distance)2 Rotational Inertia Depends upon the axis around which it rotates Easier to rotate pencil around an axis passing through it. Harder to rotate it around vertical axis passing through center. Hardest to rotate it around vertical axis passing through the end. Calculating Moment of Inertia Point-objects: I = Σm i r i 2 Solid sphere (through center): I = 2/5 MR 2 Hollow sphere (through center): I = 2/3 MR 2 Solid disk (through center): I = 1/2 MR 2 Hoop (through center) : I = MR 2 See textbook for more examples (pg. 216) Example: Hoop vs. Disk Imagine rolling a hoop and a disk of equal mass down a ramp. Which one would win? Which one is easier to rotate (i.e., has less rotational inertia)? 1

2 Torque Torque is the rotational analog of force. Same sign convention as other rotational quantities Depends on: Magnitude of Force (F) Direction of force Lever arm (r) Examples of Lever Arm Lever arm is amount of perpendicular distance to where the force acts: points from pivot point to location of force τ = r x F ( cross product ) Units: Nm Torque Forces are not always perpendicular to the lever arm! Torque definition picks out the perpendicular component of the force. τ = r perp F or = rf perp Torque is a vector quantity, can be treated in the same way as forces. A plumber attempts to tighted a bolt by exerting a force on the end of a wrench, perpendicular to the handle. Which has the largest torque? A. Wrench A: 20 cm, 10 N B. Wrench B: 40 cm, 5 N C. Wrench C: 20 cm, 5 N D. Wrench D: 40 cm, 10 N A plumber attempts to tighted a bolt by exerting a force on the end of a wrench, perpendicular to the handle. Which has the smallest torque? A. Wrench A: 20 cm, 10 N B. Wrench B: 40 cm, 5 N C. Wrench C: 20 cm, 5 N D. Wrench D: 40 cm, 10 N Right Hand Rule for Torque Point the fingers in the direction of the position vector Curl the fingers toward the force vector The thumb points in the direction of the torque 2

3 Torque Example A plumber attempts to loosen a bolt by pushing downward on a wrench angled 30º below the horizontal. If she can exert 75 N of force, compare the torque with the wrench at 30º to the torque if the wrench was completely horizontal. Revisiting Newton s Laws 1: Need a linear force to change an object s linear motion Need a torque to change an object s rotational motion Equilibrium: Linear: ΣF = 0 Rotational: Στ = 0 2: Translational acceleration ~ force, and ~ 1/mass Angular acceleration ~ torque, and ~ 1/rotational inertia Example: See-Saw Balancing 4 m? m Agenda Today: Center of gravity, torque and rotation worksheet, rolling without slipping Tuesday: Homework #7 quiz, statics and springs Center of Gravity Average position of all the mass in an object is called the center of mass (CG) of object. F g acts at the center of gravity important for torque! Calculating CG x cm = x 1 m 1 + x 2 m 2 + /(m tot ) y cm = y 1 m 1 + y 2 m 2 + /(m tot ) Center of mass/center of gravity can also be found experimentally by balancing/hanging an object. 3

4 Example: Where is the CG for each of these objects (assume rods are massless and 50 cm long, m= 1kg)? Example of a Free Body Diagram (Forearm) Example of a Free Body Diagram (Ladder) Example: Rank net torque about each pivot from least to greatest. The free body diagram shows the normal force and the force of static friction acting on the ladder at the ground The last diagram shows the lever arms for the forces Example Three trucks are parked on a slope. Which truck(s) tip over? A. Left truck B. Middle truck C. Right truck D. Both B and C E. All three Newton s Second Law for a Rotating Object Σ τ = Iα The angular acceleration is directly proportional to the net torque The angular acceleration is inversely proportional to the moment of inertia of the object Combine with F = ma for full statics problems 4

5 Example: Rod with two masses Rolling without slipping Two points masses, m 1 = 1kg and m 2 = 2kg, are suspended from a massless rod of total length L = 1m. The rod s pivot point is fixed a distance d = 0.25m from the left end (see diagram on the board). Find a group of people (no more than 3) to work with, and get as far through the problem as you can over the next 15 minutes. Discuss your approach with your group, and follow the general problemsolving strategy. Raise your hand if your group gets stuck, and I will come around to help. Rolling without slipping If the object completes one rotation, its center will move a linear distance of exactly one circumference: Δx = 2πr This gives us a relationship between linear velocity (of the center of the object) and angular velocity: v = 2πr/Δt = ωr Rolling without Slipping Applications: string unwinding from a cylinder or pulley Wheels on the road: connect linear motion and rotation Careful: don t apply v= rω blindly, or for any old location on the rolling object! Ask yourself if it makes sense for the problem. Example: Spinning your tires Consider a spot on the top of a car tire with radius 65 cm. If the car is stuck in the mud and the wheels just spin, what is happening? What is different when the tires get traction and start to roll without slipping? - Location of pivot point - Speed of the point at the top of the tire 5

### 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

### Rotational Motion. Chapter 8: Rotational Motion. Angular Position. Rotational Motion. Ranking: Rolling Cups 9/21/12 Rotational Motion Chapter 8: Rotational Motion In physics we distinguish two types of motion for objects: Translational Motion (change of location): Whole object moves through space. Rotational Motion

### 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

### 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

### Chapter 8 - Rotational Dynamics and Equilibrium REVIEW Pagpalain ka! (Good luck, in Filipino) Date Chapter 8 - Rotational Dynamics and Equilibrium REVIEW TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) When a rigid body

### 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

### 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

### 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.

### 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

### 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

### Physics 8 Friday, November 4, 2011 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

### Chapter 9 Rotational Dynamics Chapter 9 ROTATIONAL DYNAMICS PREVIEW A force acting at a perpendicular distance from a rotation point, such as pushing a doorknob and causing the door to rotate on its hinges, produces a torque. If the

### 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

### Physics 111. Tuesday, November 2, Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy ics Tuesday, ember 2, 2002 Ch 11: Rotational Dynamics Torque Angular Momentum Rotational Kinetic Energy Announcements Wednesday, 8-9 pm in NSC 118/119 Sunday, 6:30-8 pm in CCLIR 468 Announcements This

### Rotational N.2 nd Law Lecture 0 Chapter 1 Physics I Rotational N. nd Law Torque Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will continue discussing rotational dynamics Today

### 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

### Chapter 9. Rotational Dynamics Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular

### Chapter 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

### 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

### 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

### 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

### General Physics (PHY 2130) General Physics (PHY 130) Lecture 0 Rotational dynamics equilibrium nd Newton s Law for rotational motion rolling Exam II review http://www.physics.wayne.edu/~apetrov/phy130/ Lightning Review Last lecture:

### 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 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

### Announcements Oct 16, 2014 Announcements Oct 16, 2014 1. Prayer 2. While waiting, see how many of these blanks you can fill out: Centripetal Accel.: Causes change in It points but not Magnitude: a c = How to use with N2: Always

### 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

### Lecture 14. Rotational dynamics Torque. Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Lecture 14 Rotational dynamics Torque Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. Archimedes, 87 1 BC EXAM Tuesday March 6, 018 8:15 PM 9:45 PM Today s Topics:

### 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

### Phys 106 Practice Problems Common Quiz 1 Spring 2003 Phys 106 Practice Problems Common Quiz 1 Spring 2003 1. For a wheel spinning with constant angular acceleration on an axis through its center, the ratio of the speed of a point on the rim to the speed

### Physics 8 Monday, October 28, 2013 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

### Teach Yourself AP Physics in 24 Hours. and Equilibrium. Physics Rapid Learning Series Rapid Learning Center Chemistry :: Biology :: Physics :: Math Rapid Learning Center Presents Teach Yourself AP Physics in 4 Hours 1/53 *AP is a registered trademark of the College Board, which does not

### 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

### Rotational N.2 nd Law Lecture 19 Chapter 12 Rotational N.2 nd Law Torque Newton 2 nd Law again!? That s it. He crossed the line! Course website: http://faculty.uml.edu/andriy_danylov/teaching/physicsi IN THIS CHAPTER, you will

### Chapter 8 Rotational Motion and Equilibrium. 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction Chapter 8 Rotational Motion and Equilibrium Name 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction 1. The distance between a turning axis and the

### Physics. Chapter 8 Rotational Motion 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

### Rotation Quiz II, review part A Rotation Quiz II, review part A 1. A solid disk with a radius R rotates at a constant rate ω. Which of the following points has the greater angular velocity? A. A B. B C. C D. D E. All points have the

### Chapter 8, Rotational Equilibrium and Rotational Dynamics. 3. If a net torque is applied to an object, that object will experience: CHAPTER 8 3. If a net torque is applied to an object, that object will experience: a. a constant angular speed b. an angular acceleration c. a constant moment of inertia d. an increasing moment of inertia

### 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

### O Which force produces the greatest torque about the point O (marked by the blue dot)? Q10.1 The four forces shown all have the same magnitude: F 1 = F 2 = F 3 = F 4. F 1 F 3 O Which force produces the greatest torque about the point O (marked by the blue dot)? F 2 F 4 A. F 1 B. F 2 C. F

### 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

### = 2 5 MR2. I sphere = MR 2. I hoop = 1 2 MR2. I disk A sphere (green), a disk (blue), and a hoop (red0, each with mass M and radius R, all start from rest at the top of an inclined plane and roll to the bottom. Which object reaches the bottom first? (Use

### CHAPTER 8: 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

### PSI AP Physics I Rotational Motion 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

### 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

### PSI AP Physics I Rotational Motion 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

### 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

### Dynamics of Rotational Motion: Rotational Inertia Dynamics of Rotational Motion: Rotational Inertia Bởi: OpenStaxCollege If you have ever spun a bike wheel or pushed a merry-go-round, you know that force is needed to change angular velocity as seen in

### = F 4. O Which force produces the greatest torque about the point O (marked by the blue dot)? E. not enough information given to decide Q10.1 The four forces shown all have the same magnitude: F 1 = F 2 = F 3 = F 4. F 1 F 3 O Which force produces the greatest torque about the point O (marked by the blue dot)? F 2 F 4 A. F 1 B. F 2 C. F

### 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

### Moment of Inertia Race Review Two points, A and B, are on a disk that rotates with a uniform speed about an axis. Point A is closer to the axis than point B. Which of the following is NOT true? 1. Point B has the greater tangential

### 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 AP Physics 1- Torque, Rotational Inertia, and Angular Momentum Practice Problems FACT: The center of mass of a system of objects obeys Newton s second law- F = Ma cm. Usually the location of the center

### AP Physics 1: Rotational Motion & Dynamics: Problem Set AP Physics 1: Rotational Motion & Dynamics: Problem Set I. Axis of Rotation and Angular Properties 1. How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? 2. How many degrees are

### Chapter 11 Motion in a Circle Lecture Outline Chapter 11 Motion in a Circle Remaining Schedule (tentative) 29 Mar torque 12.1-5 31 Mar torque 12.6-8 5Apr periodic motion 15.1-7 7 Apr fluids 18.1-5 12 Apr fluids 18.6-8 14 Apr EXAM 3

### Physics 1A Lecture 10B Physics 1A Lecture 10B "Sometimes the world puts a spin on life. When our equilibrium returns to us, we understand more because we've seen the whole picture. --Davis Barton Cross Products Another way to

### 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

### 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

### AP practice ch 7-8 Multiple Choice 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

### 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

### Physics 8 Wednesday, October 25, 2017 Physics 8 Wednesday, October 25, 2017 HW07 due Friday. It is mainly rotation, plus a couple of basic torque questions. And there are only 8 problems this week. For today, you read (in Perusall) Onouye/Kane

### Exam 3 PREP Chapters 6, 7, 8 PHY241 - General Physics I Dr. Carlson, Fall 2013 Prep Exam 3 PREP Chapters 6, 7, 8 Name TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) Astronauts in orbiting satellites

### Rotation. I. Kinematics - Angular analogs Rotation I. Kinematics - Angular analogs II. III. IV. Dynamics - Torque and Rotational Inertia Work and Energy Angular Momentum - Bodies and particles V. Elliptical Orbits The student will be able to:

### 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

### 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

### It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points? A) I B) II C) III D) IV AP Physics 1 Lesson 16 Homework Newton s First and Second Law of Rotational Motion Outcomes Define rotational inertia, torque, and center of gravity. State and explain Newton s first Law of Motion as it

### Chapter 9. Rotational Dynamics Chapter 9 Rotational Dynamics In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation. 1) Torque Produces angular

### Rotational Mechanics Part III Dynamics. Pre AP Physics Rotational Mechanics Part III Dynamics Pre AP Physics We have so far discussed rotational kinematics the description of rotational motion in terms of angle, angular velocity and angular acceleration and

### Chapter 9 TORQUE & Rotational Kinematics Chapter 9 TORQUE & Rotational Kinematics This motionless person is in static equilibrium. The forces acting on him add up to zero. Both forces are vertical in this case. This car is in dynamic equilibrium

### 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

### 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.

### A. Incorrect! It looks like you forgot to include π in your calculation of angular velocity. High School Physics - Problem Drill 10: Rotational Motion and Equilbrium 1. If a bike wheel of radius 50 cm rotates at 300 rpm what is its angular velocity and what is the linear speed of a point on the

### 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

### Problem Set x Classical Mechanics, Fall 2016 Massachusetts Institute of Technology. 1. Moment of Inertia: Disc and Washer 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

### 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

### 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

### 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,

### Static Equilibrium; Torque Static Equilibrium; Torque The Conditions for Equilibrium An object with forces acting on it, but that is not moving, is said to be in equilibrium. The first condition for equilibrium is that the net force

### Rotational Dynamics. A wrench floats weightlessly in space. It is subjected to two forces of equal and opposite magnitude: Will the wrench accelerate? Rotational Dynamics A wrench floats weightlessly in space. It is subjected to two forces of equal and opposite magnitude: Will the wrench accelerate? A. yes B. no C. kind of? Rotational Dynamics 10.1-3

### Definition. is a measure of how much a force acting on an object causes that object to rotate, symbol is, (Greek letter tau) Torque Definition is a measure of how much a force acting on an object causes that object to rotate, symbol is, (Greek letter tau) = r F = rfsin, r = distance from pivot to force, F is the applied force

### Announcements Oct 27, 2009 Announcements Oct 7, 009 1. HW 14 due tonight. Reminder: some of your HW answers will need to be written in scientific notation. Do this with e notation, not with x signs. a. 6.57E33 correct format b.

### 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

### Cutnell/Johnson Physics Cutnell/Johnson Physics Classroom Response System Questions Chapter 9 Rotational Dynamics Interactive Lecture Questions 9.1.1. You are using a wrench in an attempt to loosen a nut by applying a force as

### Exercise Torque Magnitude Ranking Task. Part A Exercise 10.2 Calculate the net torque about point O for the two forces applied as in the figure. The rod and both forces are in the plane of the page. Take positive torques to be counterclockwise. τ 28.0

### PHY218 SPRING 2016 Review for Exam#3: Week 12 Review: Linear Momentum, Collisions, Rotational Motion, and Equilibrium PHY218 SPRING 2016 Review for Exam#3: Week 12 Review: Linear Momentum, Collisions, Rotational Motion, and Equilibrium These are selected problems that you are to solve independently or in a team of 2-3

### Chapters 10 & 11: Rotational Dynamics Thursday March 8 th Chapters 10 & 11: Rotational Dynamics Thursday March 8 th Review of rotational kinematics equations Review and more on rotational inertia Rolling motion as rotation and translation Rotational kinetic energy

### 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

### A Ferris wheel in Japan has a radius of 50m and a mass of 1.2 x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at Option B Quiz 1. A Ferris wheel in Japan has a radius of 50m and a mass of 1. x 10 6 kg. If a torque of 1 x 10 9 Nm is needed to turn the wheel when it starts at rest, what is the wheel s angular acceleration?

### Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow) Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow) Name (printed) Lab Section(+2 pts) Name (signed as on ID) Multiple choice Section. Circle the correct answer. No work need be shown and no partial

### Big Ideas 3 & 5: Circular Motion and Rotation 1 AP Physics 1 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

### Use the following to answer question 1: Use the following to answer question 1: On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to

### 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

### 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 Raymond A. Serway Chris Vuille Chapter Eight Rotational Equilibrium and Rotational Dynamics Application of Forces The point of application of a force is important This was ignored in treating objects as Connexions module: m42179 1 Dynamics of Rotational Motion: Rotational Inertia OpenStax College This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License