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.

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "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."

Transcription

1 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 final speed of the 70 kg ball.

2 Ch. 8: Impulse, momentum, collisions Momentum, p = mv (inertia of moving object) 2 Impulse: J = F t or Fdt 1 gives momentum change: J = p2 p1 Momentum Conservation: total P = p + p +... conserved for closed systems. Elastic vs. inelastic collisions: K conserved for elastic m1r 1 + m2r Center of mass, rcm = m1 + m CM velocity: CM moves as particle with momentum P = Mv cm (also CM has important role for acceleration of solid rotors) A B

3 Exam 3 formula sheet (2 nd page is moments of inertia)

4 Before the collision, 70 kg ball is stationary. Afterward, the 30 kg ball is moving vertically with speed v/2. 30 kg 70 kg v (a) Is this collision elastic? (b) Find the final speed and direction of the 70 kg ball.

5 A thin-walled hollow sphere, m = 12 kg & diameter = 48.0 cm, is rotating according to, θ = At 2 + Bt 4, with A = 1.50 and B = 1.00, t given in seconds. (a) What are the units of A and B? (b) At t = 2.00 s, find the angular momentum, and the torque on the sphere.

6 Chapter 9: Rotations Angular velocity, acceleration: ω = dθ angular velocity, α = dω angular acceleration. dt dt 2 Linear vs. angular relations, Vectors: v = rω atan = rα arad = ω r ω, α along axis in right hand rule direction. Constant angular acceleration: familiar formulas. θ = θ 0 + ω 0 t αt 2 analog of similar for other constant-a relations. Energy and Moment of inertia: x = x 0 + v 0 x t a x t 2 K = 1 2 Iω 2 analog of K = 1 2 mv2 I 1 = 2 mr 2 moment of inertia.

7 I = mr 2 moments of inertia same as for KE.

8 A solid spool, mass M, radius R, is held steady by a string wound around its perimeter. Spool rests with no slipping on 45 ramp. Find T in the string and the friction force. Other questions: (a) Suppose hollow cylinder instead of solid spool, but same mass M. Is T same or different? (b) Suppose string pulled s.t. string has constant velocity v, and spool rolls uphill with no slipping. Find T in this case.

9 Rotational Mechanics & Equilibrium KE = 1 2 Iω 2 (energy) τ = Iα W = τθ L = Iω (torque) Rotational form of F = ma (work) W = Fs (momentum) p = mv Substitute: θ for x I for m τ for F ω for v α for a L for p Equilibrium: F x = 0 F y = 0 τ = 0 (any axis) same as CM x = w x w = m x m cg i i i i i i

10 A solid spool, mass M, radius R, held steady by a string wound around its perimeter. Spool rests with no slipping on 45 ramp. String is cut allowing ball to roll downward without slipping. (a) Find acceleration down the ramp. (b) Find the friction force.

11 A mass is hanging from the end of a horizontal bar which pivots about an axis through it center, but it being held stationary. The bar is released and begins to rotate. As the bar rotates from horizontal to vertical, the magnitude of the angular acceleration α of the bar.. A) increases B) decreases C) remains constant

12 A mass is hanging from the end of a horizontal bar which pivots about an axis through it center, but it being held stationary. The bar is released and begins to rotate. As the bar rotates from horizontal to vertical, the magnitude of the torque on the bar.. A) increases B) decreases C) remains constant

13 Ball has m = 3.0 kg and initial v = 2.0 m/s. The rotor has total m = 5.0 kg, consists of a 3.0 kg rod, length L = 1.0 m, with a small 2.0 kg mass attached at the end. The ball strikes the rotor at its midpoint & sticks to it. pivot v (a) Is energy conserved in the collision? (b) What is the angular velocity of the rotor just after the collision? (c) What maximum angle does rotor attain?

14 Exam 3 formula sheet (2 nd page is moments of inertia)

15 Find the center of mass. 30 m 50 kg 40 m 20 kg 30 kg

16 Find the center of mass velocity, if the lower two masses are stationary. 30 m 50 kg 15 m/s 40 m 20 kg 30 kg

17 Consider a sudden elastic collision between the ball and the block. What is the maximum angle of rise of the ball when it rebounds after collision? (a) same as original θ. (b) larger. (c) smaller.

18 A grinding wheel is spinning freely at 30.0 rpm. Then, an iron bar is pushed against its edge at constant force, causing it to stop in 4.5 s. (a) Is the angular acceleration constant? (b) Find the total angle through which the wheel turns while stopping.

19 Consider masses arranged as below, with M > m. The pulley has mass m p, and is a solid disk, radius r. No friction a) Compute the acceleration and tensions T 1 and T 2 on opposite sides of the pulley.

20 Consider masses arranged as below, with M > m. The pulley has mass m p, and is a solid disk, radius r. No friction a) Compute the acceleration and tensions T 1 and T 2 on opposite sides of the pulley.

21 Consider masses arranged as below, with M > m. The pulley has mass m p, and is a solid disk, radius r. No friction a) Compute the acceleration and tensions T 1 and T 2 on opposite sides of the pulley.

22 Consider masses arranged as below, with M > m. The pulley has mass m p, and is a solid disk, radius r. No friction a) Compute the acceleration and tensions T 1 and T 2 on opposite sides of the pulley. b) Using energy methods, find the velocity after M has fallen a distance h.

23 Consider masses arranged as below, with M > m. The pulley has mass m p, and is a solid disk, radius r. No friction a) Compute the acceleration and tensions T 1 and T 2 on opposite sides of the pulley. b) Using energy methods, find the velocity after M has fallen a distance h.

24 Consider masses arranged as below, with M > m. The pulley has mass m p, and is a solid disk, radius r. No friction a) Compute the acceleration and tensions T 1 and T 2 on opposite sides of the pulley. b) Using energy methods, find the velocity after M has fallen a distance h. Note acceleration methods also work to find solution

25 The non-uniform bar has mass 30 kg and its CM is 0.75 m from the left end. The bar length is 2.00 m. Cables are attached to left end and 0.4 m from right end. Find the cable tensions.

26

27 The ideal pulley is massless, and attached to a fixed axle. The rope supports a mass M 2 as shown. The other end of the rope is tied to the plank, making an angle of 30. The plank is also supported by a fulcrum at a distance L/4 from the left end of the plank, as shown. In terms of M 1, find the value of M 2 that will allow equilibrium. M 2 M 1

28 The ideal pulley is massless, and attached to a fixed axle. The rope supports a mass M 2 as shown. The other end of the rope is tied to the plank, making an angle of 30. The plank is also supported by a fulcrum at a distance L/4 from the left end of the plank, as shown. In terms of M 1, find the value of M 2 that will allow equilibrium. Also find force on fulcrum. M 2 M 1

29 If box is 3m high and 2m wide, find initial angular acceleration. Assume the box does not slip on the support point. Also find the instantaneous force components exerted by the fulcrum. M

30 I = mr 2 moments of inertia same as for KE.

31 A tire (illustrated) has fallen from a cart and is rolling on a horizontal road with constant center of mass velocity v. Find the instantaneous velocity vector and acceleration vector for the part of the tread at the edge of the tire (arrow) at the front edge even with the center of the tire. M

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

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

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

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

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

Exam 3 Practice Solutions

Exam 3 Practice Solutions Exam 3 Practice Solutions Multiple Choice 1. A thin hoop, a solid disk, and a solid sphere, each with the same mass and radius, are at rest at the top of an inclined plane. If all three are released at

More information

A) 4.0 m/s B) 5.0 m/s C) 0 m/s D) 3.0 m/s E) 2.0 m/s. Ans: Q2.

A) 4.0 m/s B) 5.0 m/s C) 0 m/s D) 3.0 m/s E) 2.0 m/s. Ans: Q2. Coordinator: Dr. W. Al-Basheer Thursday, July 30, 2015 Page: 1 Q1. A constant force F ( 7.0ˆ i 2.0 ˆj ) N acts on a 2.0 kg block, initially at rest, on a frictionless horizontal surface. If the force causes

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

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 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

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

Physics 201 Exam 3 (Monday, November 5) Fall 2012 (Saslow)

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

More information

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 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

More information

PHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011

PHYSICS 221, FALL 2011 EXAM #2 SOLUTIONS WEDNESDAY, NOVEMBER 2, 2011 PHYSICS 1, FALL 011 EXAM SOLUTIONS WEDNESDAY, NOVEMBER, 011 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 this

More information

Concept Question: Normal Force

Concept Question: Normal Force Concept Question: Normal Force Consider a person standing in an elevator that is accelerating upward. The upward normal force N exerted by the elevator floor on the person is 1. larger than 2. identical

More information

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

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

More information

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

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

More information

Name SOLUTION Student ID Score Speed of blocks is is decreasing. Part III. [25 points] Two blocks move on a frictionless

Name SOLUTION Student ID Score Speed of blocks is is decreasing. Part III. [25 points] Two blocks move on a frictionless Name SOLUTION Student ID Score last first Speed of blocks is is decreasing. Part III. [25 points] Two blocks move on a frictionless v o incline with initial speed v o, as shown, while a hand pushes with

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

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

Your Name: PHYSICS 101 MIDTERM. Please circle your section 1 9 am Galbiati 2 10 am Kwon 3 11 am McDonald 4 12:30 pm McDonald 5 12:30 pm Kwon

Your Name: PHYSICS 101 MIDTERM. Please circle your section 1 9 am Galbiati 2 10 am Kwon 3 11 am McDonald 4 12:30 pm McDonald 5 12:30 pm Kwon 1 Your Name: PHYSICS 101 MIDTERM October 26, 2006 2 hours Please circle your section 1 9 am Galbiati 2 10 am Kwon 3 11 am McDonald 4 12:30 pm McDonald 5 12:30 pm Kwon Problem Score 1 /13 2 /20 3 /20 4

More information

Department of Physics

Department of Physics Department of Physics PHYS101-051 FINAL EXAM Test Code: 100 Tuesday, 4 January 006 in Building 54 Exam Duration: 3 hrs (from 1:30pm to 3:30pm) Name: Student Number: Section Number: Page 1 1. A car starts

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

PHYSICS 218 Final Exam Fall, 2014

PHYSICS 218 Final Exam Fall, 2014 PHYSICS 18 Final Exam Fall, 014 Name: Signature: E-mail: Section Number: No calculators are allowed in the test. Be sure to put a box around your final answers and clearly indicate your work to your grader.

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

8.012 Physics I: Classical Mechanics Fall 2008

8.012 Physics I: Classical Mechanics Fall 2008 MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE

More information

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

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

More information

On my honor, I have neither given nor received unauthorized aid on this examination.

On my honor, I have neither given nor received unauthorized aid on this examination. Instructor(s): Profs. D. Reitze, H. Chan PHYSICS DEPARTMENT PHY 2053 Exam 2 April 2, 2009 Name (print, last first): Signature: On my honor, I have neither given nor received unauthorized aid on this examination.

More information

Rolling, Torque & Angular Momentum

Rolling, Torque & Angular Momentum PHYS 101 Previous Exam Problems CHAPTER 11 Rolling, Torque & Angular Momentum Rolling motion Torque Angular momentum Conservation of angular momentum 1. A uniform hoop (ring) is rolling smoothly from the

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

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01 Physics I Fall Term 2009 Review Module on Solving N equations in N unknowns

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01 Physics I Fall Term 2009 Review Module on Solving N equations in N unknowns MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department 8.01 Physics I Fall Term 2009 Review Module on Solving N equations in N unknowns Most students first exposure to solving N linear equations in N

More information

CHAPTER 8 TEST REVIEW MARKSCHEME

CHAPTER 8 TEST REVIEW MARKSCHEME AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 Multi-Response Free Response 3 Short Free Response 2 Long Free Response MULTIPLE CHOICE DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM

More information

8.012 Physics I: Classical Mechanics Fall 2008

8.012 Physics I: Classical Mechanics Fall 2008 IT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical echanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. ASSACHUSETTS INSTITUTE

More information

Solution Only gravity is doing work. Since gravity is a conservative force mechanical energy is conserved:

Solution Only gravity is doing work. Since gravity is a conservative force mechanical energy is conserved: 8) roller coaster starts with a speed of 8.0 m/s at a point 45 m above the bottom of a dip (see figure). Neglecting friction, what will be the speed of the roller coaster at the top of the next slope,

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 111.6 MIDTERM TEST #2 November 16, 2000 Time: 90 minutes NAME: STUDENT NO.: (Last) Please Print (Given) LECTURE SECTION

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

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Common Quiz Mistakes / Practice for Final Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A ball is thrown directly upward and experiences

More information

Slide 1 / 133. Slide 2 / 133. Slide 3 / How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m?

Slide 1 / 133. Slide 2 / 133. Slide 3 / How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? 1 How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? Slide 1 / 133 2 How many degrees are subtended by a 0.10 m arc of a circle of radius of 0.40 m? Slide 2 / 133 3 A ball rotates

More information

Slide 2 / 133. Slide 1 / 133. Slide 3 / 133. Slide 4 / 133. Slide 5 / 133. Slide 6 / 133

Slide 2 / 133. Slide 1 / 133. Slide 3 / 133. Slide 4 / 133. Slide 5 / 133. Slide 6 / 133 Slide 1 / 133 1 How many radians are subtended by a 0.10 m arc of a circle of radius 0.40 m? Slide 2 / 133 2 How many degrees are subtended by a 0.10 m arc of a circle of radius of 0.40 m? Slide 3 / 133

More information

Physics 221. Exam III Spring f S While the cylinder is rolling up, the frictional force is and the cylinder is rotating

Physics 221. Exam III Spring f S While the cylinder is rolling up, the frictional force is and the cylinder is rotating Physics 1. Exam III Spring 003 The situation below refers to the next three questions: A solid cylinder of radius R and mass M with initial velocity v 0 rolls without slipping up the inclined plane. N

More information

8.012 Physics I: Classical Mechanics Fall 2008

8.012 Physics I: Classical Mechanics Fall 2008 MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE

More information

Moment of Inertia Race

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

More information

PSI AP Physics I Rotational Motion

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

More information

Plane Motion of Rigid Bodies: Momentum Methods

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

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

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

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

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

Physics Fall Mechanics, Thermodynamics, Waves, Fluids. Lecture 20: Rotational Motion. Slide 20-1

Physics Fall Mechanics, Thermodynamics, Waves, Fluids. Lecture 20: Rotational Motion. Slide 20-1 Physics 1501 Fall 2008 Mechanics, Thermodynamics, Waves, Fluids Lecture 20: Rotational Motion Slide 20-1 Recap: center of mass, linear momentum A composite system behaves as though its mass is concentrated

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

University Physics (Prof. David Flory) Chapt_11 Thursday, November 15, 2007 Page 1

University Physics (Prof. David Flory) Chapt_11 Thursday, November 15, 2007 Page 1 University Physics (Prof. David Flory) Chapt_11 Thursday, November 15, 2007 Page 1 Name: Date: 1. For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on

More information

Chapter 8. Rotational Motion

Chapter 8. Rotational Motion Chapter 8 Rotational Motion Rotational Work and Energy W = Fs = s = rθ Frθ Consider the work done in rotating a wheel with a tangential force, F, by an angle θ. τ = Fr W =τθ Rotational Work and Energy

More information

Phys101 Third Major-161 Zero Version Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1

Phys101 Third Major-161 Zero Version Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1 Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1 Q1. A water molecule (H 2O) consists of an oxygen (O) atom of mass 16m and two hydrogen (H) atoms, each of mass m, bound to it (see Figure

More information

Physics 121, Final Exam Do not turn the pages of the exam until you are instructed to do so.

Physics 121, Final Exam Do not turn the pages of the exam until you are instructed to do so. , Final Exam Do not turn the pages of the exam until you are instructed to do so. You are responsible for reading the following rules carefully before beginning. Exam rules: You may use only a writing

More information

NAME. (2) Choose the graph below that represents the velocity vs. time for constant, nonzero acceleration in one dimension.

NAME. (2) Choose the graph below that represents the velocity vs. time for constant, nonzero acceleration in one dimension. (1) The figure shows a lever (which is a uniform bar, length d and mass M), hinged at the bottom and supported steadily by a rope. The rope is attached a distance d/4 from the hinge. The two angles are

More information

PY205N Spring The vectors a, b, and c. are related by c = a b. The diagram below that best illustrates this relationship is (a) I

PY205N Spring The vectors a, b, and c. are related by c = a b. The diagram below that best illustrates this relationship is (a) I PY205N Spring 2013 Final exam, practice version MODIFIED This practice exam is to help students prepare for the final exam to be given at the end of the semester. Please note that while problems on this

More information

Assignment 9. to roll without slipping, how large must F be? Ans: F = R d mgsinθ.

Assignment 9. to roll without slipping, how large must F be? Ans: F = R d mgsinθ. Assignment 9 1. A heavy cylindrical container is being rolled up an incline as shown, by applying a force parallel to the incline. The static friction coefficient is µ s. The cylinder has radius R, mass

More information

PSI AP Physics I Rotational Motion

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

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

Physics 211 Spring 2014 Final Practice Exam

Physics 211 Spring 2014 Final Practice Exam Physics 211 Spring 2014 Final Practice Exam This exam is closed book and notes. A formula sheet will be provided for you at the end of the final exam you can download a copy for the practice exam from

More information

PHY218 SPRING 2016 Review for Final Exam: Week 14 Final Review: Chapters 1-11, 13-14

PHY218 SPRING 2016 Review for Final Exam: Week 14 Final Review: Chapters 1-11, 13-14 Final Review: Chapters 1-11, 13-14 These are selected problems that you are to solve independently or in a team of 2-3 in order to better prepare for your Final Exam 1 Problem 1: Chasing a motorist This

More information

DYNAMICS ME HOMEWORK PROBLEM SETS

DYNAMICS ME HOMEWORK PROBLEM SETS DYNAMICS ME 34010 HOMEWORK PROBLEM SETS Mahmoud M. Safadi 1, M.B. Rubin 2 1 safadi@technion.ac.il, 2 mbrubin@technion.ac.il Faculty of Mechanical Engineering Technion Israel Institute of Technology Spring

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

Physics 53 Exam 3 November 3, 2010 Dr. Alward

Physics 53 Exam 3 November 3, 2010 Dr. Alward 1. When the speed of a rear-drive car (a car that's driven forward by the rear wheels alone) is increasing on a horizontal road the direction of the frictional force on the tires is: A) forward for all

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

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

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

PHYSICS 221 SPRING EXAM 2: March 31, 2016; 8:15pm 10:15pm

PHYSICS 221 SPRING EXAM 2: March 31, 2016; 8:15pm 10:15pm PHYSICS 221 SPRING 2016 EXAM 2: March 31, 2016; 8:15pm 10:15pm Name (printed): Recitation Instructor: Section # Student ID# INSTRUCTIONS: This exam contains 25 multiple-choice questions plus 2 extra credit

More information

Chapter 10: Dynamics of Rotational Motion

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.

More information

Chapter 8 continued. Rotational Dynamics

Chapter 8 continued. Rotational Dynamics Chapter 8 continued Rotational Dynamics 8.6 The Action of Forces and Torques on Rigid Objects Chapter 8 developed the concepts of angular motion. θ : angles and radian measure for angular variables ω :

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

Write your name legibly on the top right hand corner of this paper

Write your name legibly on the top right hand corner of this paper NAME Phys 631 Summer 2007 Quiz 2 Tuesday July 24, 2007 Instructor R. A. Lindgren 9:00 am 12:00 am Write your name legibly on the top right hand corner of this paper No Books or Notes allowed Calculator

More information

Equilibrium: Forces and Torques

Equilibrium: Forces and Torques Practice 15B Answers are available in the classroom and on the website. Scan this QR code for a direct link. Equilibrium: Forces and Torques 16. Lynn walks across a 9.0 m long plank bridge. The mass of

More information

AP Physics 1: Rotational Motion & Dynamics: Problem Set

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

More information

Exam 2 Solutions. PHY2048 Spring 2017

Exam 2 Solutions. PHY2048 Spring 2017 Exam Solutions. The figure shows an overhead view of three horizontal forces acting on a cargo canister that was initially stationary but that now moves across a frictionless floor. The force magnitudes

More information

Rolling, Torque, and Angular Momentum

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

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

TOPIC D: ROTATION EXAMPLES SPRING 2018

TOPIC D: ROTATION EXAMPLES SPRING 2018 TOPIC D: ROTATION EXAMPLES SPRING 018 Q1. A car accelerates uniformly from rest to 80 km hr 1 in 6 s. The wheels have a radius of 30 cm. What is the angular acceleration of the wheels? Q. The University

More information

Solution to phys101-t112-final Exam

Solution to phys101-t112-final Exam 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

More information

FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Monday, 14 December 2015, 6 PM to 9 PM, Field House Gym

FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Monday, 14 December 2015, 6 PM to 9 PM, Field House Gym FALL TERM EXAM, PHYS 111, INTRODUCTORY PHYSICS I Monday, 14 December 015, 6 PM to 9 PM, Field House Gym NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 13 pages. Make sure none are missing. There

More information

5. Plane Kinetics of Rigid Bodies

5. Plane Kinetics of Rigid Bodies 5. Plane Kinetics of Rigid Bodies 5.1 Mass moments of inertia 5.2 General equations of motion 5.3 Translation 5.4 Fixed axis rotation 5.5 General plane motion 5.6 Work and energy relations 5.7 Impulse

More information

Chapter 8 - Rotational Dynamics and Equilibrium REVIEW

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

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

Class XI Chapter 7- System of Particles and Rotational Motion Physics

Class XI Chapter 7- System of Particles and Rotational Motion Physics Page 178 Question 7.1: Give the location of the centre of mass of a (i) sphere, (ii) cylinder, (iii) ring, and (iv) cube, each of uniform mass density. Does the centre of mass of a body necessarily lie

More information

Name (please print): UW ID# score last first

Name (please print): UW ID# score last first 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

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

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

= 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

PHYSICS 221 Fall 2016 EXAM 2: November 02, :15pm 10:15pm. Name (printed): Recitation Instructor: Section #:

PHYSICS 221 Fall 2016 EXAM 2: November 02, :15pm 10:15pm. Name (printed): Recitation Instructor: Section #: PHYSICS 221 Fall 2016 EXAM 2: November 02, 2016 8:15pm 10:15pm Name (printed): Recitation Instructor: Section #: INSTRUCTIONS: This exam contains 25 multiple-choice questions, plus 2 extra-credit questions,

More information

16.07 Dynamics. Problem Set 10

16.07 Dynamics. Problem Set 10 NAME :..................... Massachusetts Institute of Technology 16.07 Dynamics Problem Set 10 Out date: Nov. 7, 2007 Due date: Nov. 14, 2007 Problem 1 Problem 2 Problem 3 Problem 4 Study Time Time Spent

More information

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

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

Rotation and Translation Challenge Problems Problem 1:

Rotation and Translation Challenge Problems Problem 1: Rotation and Translation Challenge Problems Problem 1: A drum A of mass m and radius R is suspended from a drum B also of mass m and radius R, which is free to rotate about its axis. The suspension is

More information

Rotational Dynamics Smart Pulley

Rotational Dynamics Smart Pulley Rotational Dynamics Smart Pulley The motion of the flywheel of a steam engine, an airplane propeller, and any rotating wheel are examples of a very important type of motion called rotational motion. If

More information

Phys 2210 S18 Practice Exam 3: Ch 8 10

Phys 2210 S18 Practice Exam 3: Ch 8 10 1. As a 1.0-kg object moves from point A to point B, it is acted upon by a single conservative force which does 40 J of work during this motion. At point A the speed of the particle is 6.0 m/s and the

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

第 1 頁, 共 7 頁 Chap10 1. Test Bank, Question 3 One revolution per minute is about: 0.0524 rad/s 0.105 rad/s 0.95 rad/s 1.57 rad/s 6.28 rad/s 2. *Chapter 10, Problem 8 The angular acceleration of a wheel

More information