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


 Buck McCoy
 4 years ago
 Views:
Transcription
1 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 is rolling without slipping at 2 m/s on a horizontal ball return. It continues to roll without slipping up a hill to a height h before momentarily coming to rest and then rolling back down the hill. What is the value of h (in cm) if you model the bowling ball as a uniform sphere with I = 2mR 2 /5 around the sphere s center of mass? (A) 29 (B) 40 (C) 58 (D) 70 (E) none of AD Conserve energy: mv 2 /2 + I 2 /2 = mgh, where I = 2mR 2 /5 and =v/r Thus, mv 2 /2 + (2mR 2 /5) (v/r) 2 /2 = mgh h = 7v 2 /(10g) =.29 m = 29 cm. The equations were setup in class 2. (5 pts) A rigid body is in equilibrium if A. F net ext = 0 B. net ext = 0 C. neither A nor B. D. either A or B. E. both A and B. 3. (5 pts) Determine the moment of inertia of a uniform solid sphere (about its CM, I = 2MR 2 /5) of mass M and radius R about an axis that is tangent to the surface of the sphere as shown. (A) MR 2 /2 (B) 7MR 2 /5 (C) 2MR 2 /3 (D) 35MR 2 /108 (E) 29MR 2 /110 Use the Parallel Axis Thm: I = I cm + MR 2 = 2MR 2 /5 +MR 2 = 7MR 2 /5 WebAssign homework
2 Question II. (25 pts) Torque and Angular Momentum 4. (5 pts) Rank in order, from largest to smallest, the five torques a thru e. The rods all have the same length and are pivoted at the dot. 2N 2N 2N 4N (a) (b) (c) (d) (e) N (A) e > a = d > b > c (B) d e a b c (C) d e a b c (D) d c a b c (E e a d b c only if one chooses the moment arm for (d) to be less than half the distance compared to case (a) 5. (5 pts) Two buckets spin around in a horizontal circle on frictionless bearings as shown. Suddenly, it starts to rain with vertical drops. As a result, A. The buckets slow down because the angular momentum of the bucket + rain system is conserved. B. The buckets continue to rotate at constant angular velocity because the rain is falling vertically while the buckets move in a horizontal plane. C. The buckets continue to rotate at constant angular velocity because the total mechanical energy of the bucket + rain system is conserved. D. The buckets speed up because the potential energy of the rain is transformed into kinetic energy. E. None of the above. 6. (5 pts) A uniform disc in the xy plane of radius 20 m and mass 1200 kg rotates at 0.75 rad/s about its axis, which is also the zaxis, as shown. When viewed from a point on the positive zaxis, the disc rotates counterclockwise. What is the magnitude (in kg m 2 /s) and direction of the angular momentum? I disc = mr 2 /2.
3 (A) 1.8 x 10 5 k (B) 3.6 x 10 5 k (C) 1.8 x 10 5 j (D) 3.6 x 10 5 i (E) 14.4 x 10 5 k L = I = mr 2 /2 = 1.8x10 5 kgm 2 /s in the positive z direction 7. (5 pts) If an object were to suddenly shrink and decrease its moment of inertia by a factor of 2 without any external force, what is the ratio of the final to initial rotational kinetic energies? (A) 3 (B) 9 (C) 8 (D) 2 (E) 1 8. (5 pts) Disc 1 is rotating freely and has an angular velocity i = 0.5 rev/s about an axis that coincides with its symmetry axis as shown. Its moment of inertia is I 1 = 20 kg m 2. It drops onto disc 2, of moment of inertia I 2 = 20 kg m 2, that is initially at rest. Disc 2 is centered on the same axis as disc 1 and is free to rotate about the axis. Because of kinetic friction, the two discs eventually attain a common angular velocity f. What is f (in rev/s)? (A) 1.5 (B) 1.0 (C) 0.5 (D) 0.25 (E) Worked out in class. Conserve angular momentum L i = L f I 1 i = (I 1 + I 2 ) f So w f = I 1 w i /[I 1 + I 2 ) = 0.25 rev/s
4 Question III. (15 pts) Rotational Dynamics 9. (5 pts) Consider the inclined plane shown (not to scale). A wheel of radius 0.20 m is mounted on a frictionless horizontal axis through its geometric center. A massless cord is wrapped around the wheel and attached to an object of mass m = 2.0 kg that slides on a frictionless surface inclined at = 20 0 with the horizontal, as shown. The object accelerates down the incline at 2.0 m/s 2. What is the value, in units of kgm 2, of the rotational inertia of the wheel about its axis of rotation? (A) 5 (B) 2 (C) (D) (E) 14.6 For the sliding block, mgsin(20 0 ) T = ma and for the pulley, Tr = I or T = Ia/r 2 Substituting for T and solving for I gives I = [mgsin(20 0 ) ma]r 2 /a = 0.054kgm (5 pts) A seesaw is comprised of a massless stiff board of length L = 3 m with two point masses placed on it. One point mass, m 1 = 20 kg, is placed at one end of the board and the other point mass, m 2 = 40 kg, is placed on the other end of the board 3 m away. The fulcrum is located 1 m from the end where m 2 is located. Where must a third mass, M = 10 kg, be placed to balance the seesaw? (A) 1.5 m from m 1 (B) 0.5 m from m 2 (C) on fulcrum (D) 0.2 m between fulcrum and m 1 (E) 0.2 m between fulcrum and m 2 The torques clockwise must equal the torques counterclockwise. Choose the pivot point to be at the fulcrum. So, m 2 g(1m) =Mgx + m 1 g(2m) x = (5 pts) If m 2 is changed from 40 kg to 60 kg in question 9, where should mass M be placed to balance the seesaw? (A) on top of m 1 (B) 0.2 m from fulcrum (C) 0.5 m from m 1 (D) on top of m 2 (E) close to but not on top of m 2
5 Question IV Free Response (25 pts) Show all work in sufficient detail that the grader (Prof. Buck) understands exactly what you are calculating. Homework Problem and setup in class A large gate weighing 175 N is supported by hinges at the top and bottom of the wooden frame, and is further supported by a wire. (Assume the positive xdirection is to the right and the ydirection is upward.) 1.5 m T 45 0 F 1 F2 1.5 m F R 3m mg You can choose where to place the pivot point. Consider the pivot point to be at top hinge. The conditions for equilibrium: F = 0 F 1 + F 2 + Tsin45 = mg AND F R = Tcos45 (2) = 0 F R (1.5m) + Tsin45 (1.5m) = mg (1.5m) (a) (10 pts) What must the tension in the wire be for the force on the upper hinge to have no horizontal component? Since F R = Tcos45, then substitute into torgue equation gives Tcos45 + Tsin45 = mg (the lengths divide out). Thus T = mg/(cos45 + sin45) = 124N (b) (7 pts) What is the horizontal force on the lower hinge? (Take the direction of pushing the gate away from the hinges to be positive and the direction of pulling the gate towards
6 the hinges to be negative.) F R = Tcos45= 87.5 N (c) (8 pts) What is the sum of the vertical forces on the hinges? From the first of the force equations: F 1 + F 2 + Tsin45 = mg Thus, F 1 + F 2 = mg  Tsin45 = 175N 87.5N = 87.5 N Note: you will get the same answer even if you chose only one vertical force on just one of the hinges. It also would not matter if one hinge force was up and the other down or even both were chosen to be down. Finally, it matters not where you pick your pivot point.
7 Name Student ID last first V [20 points] Tutorial. In case 1, a puck of mass m, radius r, and uniform mass density is moving with velocity toward a disk of mass M and radius R Case 1 as shown in the topview diagram at right. The disk is at rest, and neither the puck nor the disk is rotating. m, r In this problem, you will consider 6 other cases that differ from case 1 in one or two ways. All differences will be made explicit (i.e., if any quantities are not explicitly mentioned, they have the same value in the two cases being considered). In this problem, take angular momentum to mean angular momentum of the system of all objects in that case with respect to the disc s center at the instant shown. 1 [4 pts] The velocity of the puck in case 2 is in a different direction than that in case 1 as shown at right (but the speed is the same). momentum in case 2 compare to that in case 1? 2 2 C. L 2 Case 1 r Case 2 L X = p r. The two pucks have the same mass, speed, and thus the same p. However, r is smaller for case 2. r 2. [3 pts] The speed of the puck in case 3 is twice that in case 1. momentum in case 3 compare to that in case 1? 3 3 C. L 3 3. [3 pts] The puck in case 4 is closer to the disk than in case 1 as shown at right. momentum in case 4 compare to that in case 1? 4 4 C. L 4 Case 1 Case 3 2 L X = p r. The two pucks have the same mass but the speed is twice as large in case 3, thus p is twice as large. The pucks have the same r. Case 1 Case 4 L X = p r. The two pucks have the same mass, and speed, and thus the same p. They also have the same r. B PHYS 121A Exam 3 MEUWB149A094TEF(CNL)_SOL.doc
8 Name Student ID last first 4. [3 pts] The radius of the puck in case 5 is twice that in case 1 (but the masses are the same). momentum in case 5 compare to that in case 1? 5 5 C. L 5 5. [4 pts] The mass of the puck in case 6 is twice that in case 1, and its location is different as shown at right. momentum in case 6 compare to that in case 1? 6 6 C. L 6 6. [3 pts] In case 7, the disk is removed. momentum of the puck in case 7 compare to that of the puckdisk system in case 1? 7 7 C. L 7 Case 1 Case 5 m, r m, 2r L X = p r. The two pucks have the same mass, and speed, and thus the same p. They also have the same r. Since the puck is not rotating, how its mass is distributed about its center of mass does not affect its angular momentum. Case 1 Case 6 m 2m L X = p r. The two pucks have the same speed, but the mass is twice as large in case 6, thus p is twice as large in that case. However, r is half as large in that case. Case 1 Case 7 Disk is removed The disk is at rest, thus the magnitude of its angular momentum is zero. Therefore its presence (or absence) does not affect the angular momentum of the system. B PHYS 121A Exam 3 MEUWB149A094TEF(CNL)_SOL.doc
1 MR SAMPLE EXAM 3 FALL 2013
SAMPLE EXAM 3 FALL 013 1. A merrygoround 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 informationWebreview 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 0.30mradius automobile
More informationMoment 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 informationRotation. 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 informationRolling, 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 informationChapter 12. Rotation of a Rigid Body
Chapter 12. Rotation of a Rigid Body Not all motion can be described as that of a particle. Rotation requires the idea of an extended object. This diver is moving toward the water along a parabolic trajectory,
More informationPhysics 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= o + t = ot + ½ t 2 = o + 2
Chapters 89 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 informationCHAPTER 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 informationChapter 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 informationPhys 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 informationChapter 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 informationSuggested 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 informationName: Date: Period: AP Physics C Rotational Motion HO19
1.) A wheel turns with constant acceleration 0.450 rad/s 2. (99) 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 informationPhysics 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 informationTest 7 wersja angielska
Test 7 wersja angielska 7.1A One revolution is the same as: A) 1 rad B) 57 rad C) π/2 rad D) π rad E) 2π rad 7.2A. If a wheel turns with constant angular speed then: A) each point on its rim moves with
More informationSummer 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 informationPhys101 Second Major173 Zero Version Coordinator: Dr. M. AlKuhaili Thursday, August 02, 2018 Page: 1. = 159 kw
Coordinator: Dr. M. AlKuhaili Thursday, August 2, 218 Page: 1 Q1. A car, of mass 23 kg, reaches a speed of 29. m/s in 6.1 s starting from rest. What is the average power used by the engine during the
More informationUniversity 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 informationUse 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
More informationRotation 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 informationPhysics 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 informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion MultipleChoice 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 informationKing Fahd University of Petroleum and Minerals Physics Department Physics 101 Recitation Term 131 Fall 013 Quiz # 4 Section 10 A 1.50kg block slides down a frictionless 30.0 incline, starting from rest.
More informationis acting on a body of mass m = 3.0 kg and changes its velocity from an initial
PHYS 101 second major Exam Term 102 (Zero Version) Q1. A 15.0kg block is pulled over a rough, horizontal surface by a constant force of 70.0 N acting at an angle of 20.0 above the horizontal. The block
More informationChapter 910 Test Review
Chapter 910 Test Review Chapter Summary 9.2. The Second Condition for Equilibrium Explain torque and the factors on which it depends. Describe the role of torque in rotational mechanics. 10.1. Angular
More informationPhysics 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 informationRolling, Torque, Angular Momentum
Chapter 11 Rolling, Torque, Angular Momentum Copyright 11.2 Rolling as Translational and Rotation Combined Motion of Translation : i.e.motion along a straight line Motion of Rotation : rotation about a
More informationPHYSICS. Chapter 12 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 12 Lecture RANDALL D. KNIGHT Chapter 12 Rotation of a Rigid Body IN THIS CHAPTER, you will learn to understand and apply the physics
More informationPSI AP Physics I Rotational Motion
PSI AP Physics I Rotational Motion MultipleChoice 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 informationUnless otherwise specified, use g = 9.80 m/s2
Phy 111 Exam 2 March 10, 2015 Name Section University ID Please fill in your computer answer sheet as follows: 1) In the NAME grid, fill in your last name, leave one blank space, then your first name.
More informationChapter 8. Rotational Equilibrium and Rotational Dynamics. 1. Torque. 2. Torque and Equilibrium. 3. Center of Mass and Center of Gravity
Chapter 8 Rotational Equilibrium and Rotational Dynamics 1. Torque 2. Torque and Equilibrium 3. Center of Mass and Center of Gravity 4. Torque and angular acceleration 5. Rotational Kinetic energy 6. Angular
More informationChapter 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
More informationPlane Motion of Rigid Bodies: Forces and Accelerations
Plane Motion of Rigid Bodies: Forces and Accelerations Reference: Beer, Ferdinand P. et al, Vector Mechanics for Engineers : Dynamics, 8 th Edition, Mc GrawHill Hibbeler R.C., Engineering Mechanics: Dynamics,
More information8.012 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 informationPhysics 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 informationRotational 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 informationPhysics 201 Midterm Exam 3
Physics 201 Midterm Exam 3 Information and Instructions Student ID Number: Section Number: TA Name: Please fill in all the information above. Please write and bubble your Name and Student Id number on
More informationb) 2/3 MR 2 c) 3/4MR 2 d) 2/5MR 2
Rotational Motion 1) The diameter of a flywheel increases by 1%. What will be percentage increase in moment of inertia about axis of symmetry a) 2% b) 4% c) 1% d) 0.5% 2) Two rings of the same radius and
More informationPHYSICS 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 informationPHYSICS 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 righthanded Cartesian coordinate system are î, ĵ, and ˆk, respectively. In this
More informationPHY218 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 23
More informationCHAPTER 8 TEST REVIEW MARKSCHEME
AP PHYSICS Name: Period: Date: 50 Multiple Choice 45 Single Response 5 MultiResponse Free Response 3 Short Free Response 2 Long Free Response MULTIPLE CHOICE DEVIL PHYSICS BADDEST CLASS ON CAMPUS AP EXAM
More informationPY205N 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 informationAP 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 informationPhysics 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 information6. 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 informationChapter 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 informationDYNAMICS 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 informationIII. Angular Momentum Conservation (Chap. 10) Rotation. We repeat Chap. 28 with rotatiing objects. Eqs. of motion. Energy.
Chap. 10: Rotational Motion I. Rotational Kinematics II. Rotational Dynamics  Newton s Law for Rotation III. Angular Momentum Conservation (Chap. 10) 1 Toward Exam 3 Eqs. of motion o To study angular
More information8.012 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 informationBig 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 informationExam 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 informationName (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 informationAP 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 informationTorque rotational force which causes a change in rotational motion. This force is defined by linear force multiplied by a radius.
Warm up A remotecontrolled car's wheel accelerates at 22.4 rad/s 2. If the wheel begins with an angular speed of 10.8 rad/s, what is the wheel's angular speed after exactly three full turns? AP Physics
More informationChapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = rφ = Frφ Fr = τ (torque) = τφ r φ s F to x θ = 0 DEFINITION OF
More informationPhysics 53 Exam 3 November 3, 2010 Dr. Alward
1. When the speed of a reardrive 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 informationChapter 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 MFMcGrawPHY 45 Chap_10HaRotationRevised
More informationIt 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 informationQ1. For a completely inelastic twobody 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 twobody collision the kinetic energy of the objects after the collision is the same as: ) (1/) MV, where M is the
More informationBig 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 50kg boy and a 40kg girl sit on opposite ends of a 3meter seesaw. How far from the girl should the fulcrum be placed in order for the
More informationRotation. 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 informationPhys 270 Final Exam. Figure 1: Question 1
Phys 270 Final Exam Time limit: 120 minutes Each question worths 10 points. Constants: g = 9.8m/s 2, G = 6.67 10 11 Nm 2 kg 2. 1. (a) Figure 1 shows an object with moment of inertia I and mass m oscillating
More informationPHY131H1S  Class 20. Preclass reading quiz on Chapter 12
PHY131H1S  Class 20 Today: Gravitational Torque Rotational Kinetic Energy Rolling without Slipping Equilibrium with Rotation Rotation Vectors Angular Momentum Preclass reading quiz on Chapter 12 1 Last
More informationTutorBreeze.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 informationSolution 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 informationFALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Thursday, 11 December 2014, 6 PM to 9 PM, Field House Gym
FALL TERM EXAM, PHYS 1211, INTRODUCTORY PHYSICS I Thursday, 11 December 2014, 6 PM to 9 PM, Field House Gym NAME: STUDENT ID: INSTRUCTION 1. This exam booklet has 13 pages. Make sure none are missing 2.
More informationPhysics 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 informationGeneral 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 informationEquilibrium. For an object to remain in equilibrium, two conditions must be met. The object must have no net force: and no net torque:
Equilibrium For an object to remain in equilibrium, two conditions must be met. The object must have no net force: F v = 0 and no net torque: v τ = 0 Worksheet A uniform rod with a length L and a mass
More informationRotational Motion and Torque
Rotational Motion and Torque Introduction to Angular Quantities Sections 8 to 82 Introduction Rotational motion deals with spinning objects, or objects rotating around some point. Rotational motion is
More informationPhysics 2210 Fall smartphysics Rotational Statics 11/18/2015
Physics 2210 Fall 2015 smartphysics 1718 Rotational Statics 11/18/2015 τ TT = L T 1 sin 150 = 1 T 2 1L Poll 111801 τ TT = L 2 T 2 sin 150 = 1 4 T 2L 150 150 τ gg = L 2 MM sin +90 = 1 2 MMM +90 MM τ
More informationPhysics 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 informationDO NOT separate the pages of the exam containing the problems. B01: Chow B02: Fenrich B03: Schiavone. B04: Lavoie B05: Wheelock B06: Tang
Faculty of Engineering and Department of Physics ENPH 131 Final Examination Saturday, April 21, 2012; 2:00 pm 4:30 pm Universiade Pavilion Section EB01: Rows 1, 3, 5 (seats 116) Section EB02: Rows 5 (seats
More informationAP Physics 1 Rotational Motion Practice Test
AP Physics 1 Rotational Motion Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A spinning ice skater on extremely smooth ice is able
More informationRotational 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 informationFigure 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 informationQ2. A machine carries a 4.0 kg package from an initial position of d ˆ. = (2.0 m)j at t = 0 to a final position of d ˆ ˆ
Coordinator: Dr. S. Kunwar Monday, March 25, 2019 Page: 1 Q1. An object moves in a horizontal circle at constant speed. The work done by the centripetal force is zero because: A) the centripetal force
More informationOn 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 informationHandout 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 informationWork 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
More informationChapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics
Chapter 12: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational 2 / / 1/ 2 m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv 2 /
More informationEndofChapter Exercises
EndofChapter 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 informationPhysics 23 Exam 3 April 2, 2009
1. A string is tied to a doorknob 0.79 m from the hinge as shown in the figure. At the instant shown, the force applied to the string is 5.0 N. What is the torque on the door? A) 3.3 N m B) 2.2 N m C)
More informationChap. 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 informationAP practice ch 78 Multiple Choice
AP practice ch 78 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
More informationMechanics 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 informationFINAL EXAM CLOSED BOOK
Physics 7A Section 2, Fall 2008. Instructor Lanzara FINAL EXAM CLOSED BOOK GOOD LUCK! Print Name Discussion Section# or Time Signature Discussion Section GSI Student ID# Problem Points Score 1 20 2 20
More informationWe 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 informationAP 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 informationTotal 0/15. 0/1 points POE MC.17. [ ]
Sample Problems to KSEA (2383954) Current Score: 0/15 Question Points 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 0/1 Total 0/15 1. 0/1 points POE1 2000.MC.17.
More information1. An object is dropped from rest. Which of the five following graphs correctly represents its motion? The positive direction is taken to be downward.
Unless otherwise instructed, use g = 9.8 m/s 2 Rotational Inertia about an axis through com: Hoop about axis(radius=r, mass=m) : MR 2 Hoop about diameter (radius=r, mass=m): 1/2MR 2 Disk/solid cyllinder
More informationChapter 8 continued. Rotational Dynamics
Chapter 8 continued Rotational Dynamics 8.4 Rotational Work and Energy Work to accelerate a mass rotating it by angle φ F W = F(cosθ)x x = s = rφ = Frφ Fr = τ (torque) = τφ r φ s F to s θ = 0 DEFINITION
More informationWritten Homework problems. Spring (taken from Giancoli, 4 th edition)
Written Homework problems. Spring 014. (taken from Giancoli, 4 th edition) HW1. Ch1. 19, 47 19. Determine the conversion factor between (a) km / h and mi / h, (b) m / s and ft / s, and (c) km / h and m
More informationSlide 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 informationCircular 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 informationSlide 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 informationA) 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. AlBasheer 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