dx n dt =nxn±1 x n dx = n +1 I =Σmr 2 = =r p

Size: px
Start display at page:

Download "dx n dt =nxn±1 x n dx = n +1 I =Σmr 2 = =r p"

Transcription

1 SPSP 3 30 Sept 00 Name Test Group # Remember: Show all your work for full credit. Minimum of 4 steps: Draw a diagram!! What equation are you plugging into? What numbers are you substituting? What is your final answer? Ask if anything seems unclear. Vectors have magnitude and direction! or two components! Formulae and Constants: Note: bold means vector! g = 9.80 m/s = 980 cm/s G = 6.67 x 0 - N m /kg Text Eqn - vx = vx + ax t t x = x + vx ( t t )+ ax t t -6 v = v + a x x x x0 x -7 x = x0 + ( vx0 + vx) ( t t0) -8 x = x + v ( t t ) a t t 0 x 0 x 0 0 dx n dt =nxn± x n dx = xn + n + for n - f k = µ k F N f s µ s F N a c = a radial = v / r F = GM m / r W = F dr =±U F x = - du/dx K = / mv U spr = / kx p = mv F = dp/dt Impulse = F dt = p τ = r x F = r F sin θ τ = r F = r F =r p I =Σmr = r dm I = I cm + M h Page. /5. /30 3. /5 4. /35 /5

2 . (a) Fill in the table below by saying in words the name of the angular that corresponds to the given linear, then write the symbol for the angular, and give its units. I have filled in the first row as an example. Linear Name of angular Symbol for angular Units of angular x angular position θ radians mass Force p = momentum (b) For each of the linear equations given to the left below, write the analogous rotational equation in the column to the right below. linear equation rotational equation v x = v 0x + a x (x - x 0 ) K = / mv ΣF = dp dt ΣF = m a (c) Under what general circumstances is angular momentum conserved?.(a) The three objects shown below are all constructed from identical rectangular rods and have the same mass and the same maximum horizontal dimension. The axes of rotation are shown by the the heavy black lines on the left. Put these objects in order from the one with the largest moment of inertia to smallest: A B C Largest Smallest continues over Page

3 (b) Consider a thin rod of mass M and length L which can rotate around an axis located L/4 from one end. Set up the integral necessary to find the moment of inertia of the rod about the given axis. Make all of your steps clear, but it is not necessary to evaluate the integral. (c) Consider a circular hoop of mass M and radius R and negligible thickness. What is the moment of inertia of the hoop about its center of mass? (c) If the hoop is now hung off a very-thin rod as shown and allowed to rotate about a point on its edge, what is the moment of inertia of the off center hoop? rod hoop 3. A hemispherical (radius R) bowl has a rough surface with friction on its left half and a smooth frictionless surface on the right half. A nickel released from rest at height H rolls without slipping down the left half of the bowl. H (a) Write an equation which you could solve for the speed of the nickel at the lowest position. You may include the mass m and radius r of the nickel, the initial height of the nickel H and any known constants in your equation. Note: I cm = ( / )mr for the nickel. Answer may include only: m, r, H, R, known consts, v (the unknown!) (b) Does the nickel continue to rotate at it moves up the frictionless right-hand side of the bowl? yes no (Circle one.) Explain. continues over Page

4 4. A disk rotates about its central axis, and it accelerates with constant angular acceleration. At one time it is rotating at 37 rev/s. Then 83 revolutions later, its angular speed is 7 rev/s. (a) Calculate the angular acceleration. (b) Calculate the time required to complete the 83 revolutions mentioned. 5. A thin stainless steel disk (with moment of inertia kg m ) is rotating (without friction) in a horizontal plane about its center with an angular speed of.0 rad/sec. A lead block of mass 0.50 kg is dropped from a height of 50.0 cm onto the rotating disk and sticks in place (a negligible amount of instant super glue?) a distance of 5.0 cm from the axis of rotation. (a) Is mechanical energy conserved in this process? yes no (Circle one.) Why or why not? (b) Calculate the new angular speed of the disk-cube combination. continues over Page 3

5 6. A modified Atwood s machine consists of the following: two masses, connected as shown in the diagram, are released from rest; M is on a frictionless surface, and the cord does not slip on the pulley. The m (= 40 grams) falls with an acceleraton of m/s. M = 350 gr and the radius of the pulley is.54 cm. (a) What is the magnitude of the acceleration of mass? Explain m m (b) Draw the force diagrams (include the acceleration as a double arrow ); write the appropriate Newton s nd law equations for each object; calculate the value of the moment of inertia of the pulley. Bonus: What is the approximate direction of the force supporting the pulley? m m (c) Why isn t the tension in the cord between the pulley and mass equal to the tension in the cord between the pulley and mass? E N D Page 4

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 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

Lesson 8. Luis Anchordoqui. Physics 168. Thursday, October 11, 18

Lesson 8. Luis Anchordoqui. Physics 168. Thursday, October 11, 18 Lesson 8 Physics 168 1 Rolling 2 Intuitive Question Why is it that when a body is rolling on a plane without slipping the point of contact with the plane does not move? A simple answer to this question

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

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

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

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

= 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

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

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

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

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

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

. 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

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

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

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

Figure 1 Answer: = m

Figure 1 Answer: = m Q1. Figure 1 shows a solid cylindrical steel rod of length =.0 m and diameter D =.0 cm. What will be increase in its length when m = 80 kg block is attached to its bottom end? (Young's modulus of steel

More information

Forces Part 1: Newton s Laws

Forces Part 1: Newton s Laws Forces Part 1: Newton s Laws Last modified: 13/12/2017 Forces Introduction Inertia & Newton s First Law Mass & Momentum Change in Momentum & Force Newton s Second Law Example 1 Newton s Third Law Common

More information

ME 274 Spring 2017 Examination No. 2 PROBLEM No. 2 (20 pts.) Given:

ME 274 Spring 2017 Examination No. 2 PROBLEM No. 2 (20 pts.) Given: PROBLEM No. 2 (20 pts.) Given: Blocks A and B (having masses of 2m and m, respectively) are connected by an inextensible cable, with the cable being pulled over a small pulley of negligible mass. Block

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

Revolve, Rotate & Roll:

Revolve, Rotate & Roll: I. Warm-UP. Revolve, Rotate & Roll: Physics 203, Yaverbaum John Jay College of Criminal Justice, the CUNY Given g, the rate of free-fall acceleration near Earth s surface, and r, the radius of a VERTICAL

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

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

Chapter 9. Rotational Dynamics

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

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

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

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

Physics I (Navitas) FINAL EXAM Fall 2015

Physics I (Navitas) FINAL EXAM Fall 2015 95.141 Physics I (Navitas) FINAL EXAM Fall 2015 Name, Last Name First Name Student Identification Number: Write your name at the top of each page in the space provided. Answer all questions, beginning

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

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

Summer Physics 41 Pretest. Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required.

Summer Physics 41 Pretest. Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required. Summer Physics 41 Pretest Name: Shorty Shorts (2 pts ea): Circle the best answer. Show work if a calculation is required. 1. An object hangs in equilibrium suspended by two identical ropes. Which rope

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

Physics Final Exam Formulas

Physics Final Exam Formulas INSTRUCTIONS: Write your NAME on the front of the blue exam booklet. The exam is closed book, and you may have only pens/pencils and a calculator (no stored equations or programs and no graphing). Show

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

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

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

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

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

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

Q1. Which of the following is the correct combination of dimensions for energy?

Q1. Which of the following is the correct combination of dimensions for energy? Tuesday, June 15, 2010 Page: 1 Q1. Which of the following is the correct combination of dimensions for energy? A) ML 2 /T 2 B) LT 2 /M C) MLT D) M 2 L 3 T E) ML/T 2 Q2. Two cars are initially 150 kilometers

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

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

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

Phys 106 Practice Problems Common Quiz 1 Spring 2003

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

More information

2. To study circular motion, two students use the hand-held device shown above, which consists of a rod on which a spring scale is attached.

2. To study circular motion, two students use the hand-held device shown above, which consists of a rod on which a spring scale is attached. 1. A ball of mass M attached to a string of length L moves in a circle in a vertical plane as shown above. At the top of the circular path, the tension in the string is twice the weight of the ball. At

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

Advanced Higher Physics. Rotational motion

Advanced Higher Physics. Rotational motion Wallace Hall Academy Physics Department Advanced Higher Physics Rotational motion Problems AH Physics: Rotational Motion 1 2013 Data Common Physical Quantities QUANTITY SYMBOL VALUE Gravitational acceleration

More information

AP Physics. Harmonic Motion. Multiple Choice. Test E

AP Physics. Harmonic Motion. Multiple Choice. Test E AP Physics Harmonic Motion Multiple Choice Test E A 0.10-Kg block is attached to a spring, initially unstretched, of force constant k = 40 N m as shown below. The block is released from rest at t = 0 sec.

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

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 101: Lecture 13 Rotational Kinetic Energy and Rotational Inertia. Physics 101: Lecture 13, Pg 1

Physics 101: Lecture 13 Rotational Kinetic Energy and Rotational Inertia. Physics 101: Lecture 13, Pg 1 Physics 0: Lecture 3 Rotational Kinetic Energy and Rotational Inertia Physics 0: Lecture 3, Pg Overview of Semester Newton s Laws F Net = m a Work-Energy F Net = m a W Net = DKE multiply both sides by

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

Chapter 8 Rotational Motion and Dynamics Reading Notes

Chapter 8 Rotational Motion and Dynamics Reading Notes Name: Chapter 8 Rotational Motion and Dynamics Reading Notes Section 8-1: Angular quantities A circle can be split into pieces called degrees. There are 360 degrees in a circle. A circle can be split into

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 15, 2001 Time: 90 minutes NAME: STUDENT NO.: (Last) Please Print (Given) LECTURE SECTION

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

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

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

Physics 351, Spring 2015, Homework #5. Due at start of class, Friday, February 20, 2015 Course info is at positron.hep.upenn.

Physics 351, Spring 2015, Homework #5. Due at start of class, Friday, February 20, 2015 Course info is at positron.hep.upenn. Physics 351, Spring 2015, Homework #5. Due at start of class, Friday, February 20, 2015 Course info is at positron.hep.upenn.edu/p351 When you finish this homework, remember to visit the feedback page

More information

General Physics 1. School of Science, University of Tehran Fall Exercises (set 07)

General Physics 1. School of Science, University of Tehran Fall Exercises (set 07) General Physics 1 School of Science, University of Tehran Fall 1396-97 Exercises (set 07) 1. In Fig., wheel A of radius r A 10cm is coupled by belt B to wheel C of radius r C 25 cm. The angular speed of

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

Name Student ID Score Last First. I = 2mR 2 /5 around the sphere s center of mass?

Name Student ID Score Last First. I = 2mR 2 /5 around the sphere s center of mass? NOTE: ignore air resistance in all Questions. In all Questions choose the answer that is the closest!! Question I. (15 pts) Rotation 1. (5 pts) A bowling ball that has an 11 cm radius and a 7.2 kg mass

More information

PHYSICS FORMULAS. A. B = A x B x + A y B y + A z B z = A B cos (A,B)

PHYSICS FORMULAS. A. B = A x B x + A y B y + A z B z = A B cos (A,B) PHYSICS FORMULAS A = A x i + A y j Φ = tan 1 A y A x A + B = (A x +B x )i + (A y +B y )j A. B = A x B x + A y B y + A z B z = A B cos (A,B) linear motion v = v 0 + at x - x 0 = v 0 t + ½ at 2 2a(x - x

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

SOLUTION di x = y2 dm. rdv. m = a 2 bdx. = 2 3 rpab2. I x = 1 2 rp L0. b 4 a1 - x2 a 2 b. = 4 15 rpab4. Thus, I x = 2 5 mb2. Ans.

SOLUTION di x = y2 dm. rdv. m = a 2 bdx. = 2 3 rpab2. I x = 1 2 rp L0. b 4 a1 - x2 a 2 b. = 4 15 rpab4. Thus, I x = 2 5 mb2. Ans. 17 4. Determine the moment of inertia of the semiellipsoid with respect to the x axis and express the result in terms of the mass m of the semiellipsoid. The material has a constant density r. y x y a

More information

Notes on Torque. We ve seen that if we define torque as rfsinθ, and the N 2. i i

Notes on Torque. We ve seen that if we define torque as rfsinθ, and the N 2. i i Notes on Torque We ve seen that if we define torque as rfsinθ, and the moment of inertia as N, we end up with an equation mr i= 1 that looks just like Newton s Second Law There is a crucial difference,

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

Rotational Mechanics Part III Dynamics. Pre AP Physics

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

More information

24/06/13 Forces ( F.Robilliard) 1

24/06/13 Forces ( F.Robilliard) 1 R Fr F W 24/06/13 Forces ( F.Robilliard) 1 Mass: So far, in our studies of mechanics, we have considered the motion of idealised particles moving geometrically through space. Why a particular particle

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

Anna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions.

Anna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions. Anna University May/June 2013 Exams ME2151 Engineering Mechanics Important Questions 1. Find the resultant force and its direction for the given figure 2. Two forces are acting at a point O as shown in

More information

Chapter 10: Rotation

Chapter 10: Rotation Chapter 10: Rotation Review of translational motion (motion along a straight line) Position x Displacement x Velocity v = dx/dt Acceleration a = dv/dt Mass m Newton s second law F = ma Work W = Fdcosφ

More information

Physics UCSB TR 2:00-3:15 lecture Final Exam Wednesday 3/17/2010

Physics UCSB TR 2:00-3:15 lecture Final Exam Wednesday 3/17/2010 Physics @ UCSB TR :00-3:5 lecture Final Eam Wednesday 3/7/00 Print your last name: Print your first name: Print your perm no.: INSTRUCTIONS: DO NOT START THE EXAM until you are given instructions to do

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

Mechanics II. Which of the following relations among the forces W, k, N, and F must be true?

Mechanics II. Which of the following relations among the forces W, k, N, and F must be true? Mechanics II 1. By applying a force F on a block, a person pulls a block along a rough surface at constant velocity v (see Figure below; directions, but not necessarily magnitudes, are indicated). Which

More information

Physics 5A Final Review Solutions

Physics 5A Final Review Solutions Physics A Final Review Solutions Eric Reichwein Department of Physics University of California, Santa Cruz November 6, 0. A stone is dropped into the water from a tower 44.m above the ground. Another stone

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

Show all work in answering the following questions. Partial credit may be given for problems involving calculations.

Show all work in answering the following questions. Partial credit may be given for problems involving calculations. Physics 3210, Spring 2017 Exam #1 Name: Signature: UID: Please read the following before continuing: Show all work in answering the following questions. Partial credit may be given for problems involving

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

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

NAME NUMBER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002. PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2 Q2 Q3 Total 40%

NAME NUMBER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002. PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2 Q2 Q3 Total 40% NAME NUMER SEC. PHYCS 101 SUMMER 2001/2002 FINAL EXAME:24/8/2002 PART(I) 25% PART(II) 15% PART(III)/Lab 8% ( ) 2.5 Q1 ( ) 2 Q2 Q3 Total 40% Use the followings: Magnitude of acceleration due to gravity

More information

z F 3 = = = m 1 F 1 m 2 F 2 m 3 - Linear Momentum dp dt F net = d P net = d p 1 dt d p n dt - Conservation of Linear Momentum Δ P = 0

z F 3 = = = m 1 F 1 m 2 F 2 m 3 - Linear Momentum dp dt F net = d P net = d p 1 dt d p n dt - Conservation of Linear Momentum Δ P = 0 F 1 m 2 F 2 x m 1 O z F 3 m 3 y Ma com = F net F F F net, x net, y net, z = = = Ma Ma Ma com, x com, y com, z p = mv - Linear Momentum F net = dp dt F net = d P dt = d p 1 dt +...+ d p n dt Δ P = 0 - Conservation

More information

3. Kinetics of Particles

3. Kinetics of Particles 3. Kinetics of Particles 3.1 Force, Mass and Acceleration 3.3 Impulse and Momentum 3.4 Impact 1 3.1 Force, Mass and Acceleration We draw two important conclusions from the results of the experiments. First,

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

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 53 Summer Final Exam. Solutions

Physics 53 Summer Final Exam. Solutions Final Exam Solutions In questions or problems not requiring numerical answers, express the answers in terms of the symbols given, and standard constants such as g. If numbers are required, use g = 10 m/s

More information

- 1 -APPH_MidTerm. Mid - Term Exam. Part 1: Write your answers to all multiple choice questions in this space. A B C D E A B C D E

- 1 -APPH_MidTerm. Mid - Term Exam. Part 1: Write your answers to all multiple choice questions in this space. A B C D E A B C D E Name - 1 -APPH_MidTerm AP Physics Date Mid - Term Exam Part 1: Write your answers to all multiple choice questions in this space. 1) 2) 3) 10) 11) 19) 20) 4) 12) 21) 5) 13) 22) 6) 7) 14) 15) 23) 24) 8)

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

Connection between angular and linear speed

Connection between angular and linear speed Connection between angular and linear speed If a point-like object is in motion on a circular path of radius R at an instantaneous speed v, then its instantaneous angular speed ω is v = ω R Example: A

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

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

DO NOT TURN PAGE TO START UNTIL TOLD TO DO SO.

DO NOT TURN PAGE TO START UNTIL TOLD TO DO SO. University of California at Berkeley Physics 7A Lecture 1 Professor Lin Spring 2006 Final Examination May 15, 2006, 12:30 PM 3:30 PM Print Name Signature Discussion Section # Discussion Section GSI Student

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

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. Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Two men, Joel and Jerry, push against a wall. Jerry stops after 10 min, while Joel is

More information

Final Exam. June 10, 2008, 1:00pm

Final Exam. June 10, 2008, 1:00pm PHYSICS 101: Fundamentals of Physics Final Exam Final Exam Name TA/ Section # June 10, 2008, 1:00pm Recitation Time You have 2 hour to complete the exam. Please answer all questions clearly and completely,

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

Handout 6: Rotational motion and moment of inertia. Angular velocity and angular acceleration

Handout 6: Rotational motion and moment of inertia. Angular velocity and angular acceleration 1 Handout 6: Rotational motion and moment of inertia Angular velocity and angular acceleration In Figure 1, a particle b is rotating about an axis along a circular path with radius r. The radius sweeps

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

AP Physics C! name I CM R 2. v cm K = m

AP Physics C! name I CM R 2. v cm K = m AP Physics C! name 120pt TAKE HOME TEST Chap 11 Rolling Mot., Angular Mom., Torque 3/9-14/12 Show your work on the problems Box in answers No Naked Numbers! 80pts from Chap 11 in class Questions and Problems:

More information