# Rotation Quiz II, review part A

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1 Rotation Quiz II, review part A 1. A solid disk with a radius R rotates at a constant rate ω. Which of the following points has the greater angular velocity? A. A B. B C. C D. D E. All points have the same angular velocity 2. A solid disk with a radius R rotates at a constant rate ω. Which of the following points has the greater linear velocity? A. A B. B C. C D. D E. All points have the same linear velocity

2 3. A solid disk with a radius R rotates at a constant rate ω. Which of the following represents the period of rotation? A. 2πω B. ω 2π C. 2π ω D. 2ω E. 2π 4. An object starts from rest accelerates at a constant rate α in a circular path with a radius R. The radius describes an angle θ after time t. Which of the following represents the angular velocity as a function of θ? A. 2θα B. 2 θα C. 2θ α D. 2θα E. 2θ α 5. An object starts from rest accelerates at a constant rate in a circular path. After a certain time t the object reaches the angular velocity ω. How many revolutions did it make during time t? A. 4πω B. 4ω πt C. ωt 4π D. ω t E. 4ωt

3 6. A rod with a length L with respect to point A. An external force F is applied perpendicular to the rod. In which of the following cases the torque on the rod the same as the original? A. B. C. D. E. 7. A force with a magnitude F is applied to a doorknob, a second force 2F is applied to the same door at the midpoint. Both forces are perpendicular to the door plane. Which of the following is the correct ratio between the torque of the first force and the torque of the second force? A. 2 1 B. 1 2 C. 4 1 D. 1 4 E. 1 1

4 8. Two uniform disks have the same mass but different radii: disk 1 has a Radius R, disk 2 has a radius 2R. What is the ratio between the moment of inertia of the second disk and the first disk? A. 1 2 B. 1 4 C. 2 1 D. 4 1 E When a solid object rotates with a constant angular acceleration, which of the following is true? A. All points rotate with the same centripetal acceleration B. The net torque applied to the object must be zero C. The net torque applied to the object must be non-zero and constant D. The net torque applied to the object must increase E. The net torque applied to the object must decrease 10. A bicycle wheel of radius R rolls with a constant angular velocity on a horizontal surface without friction. Which of the following is the right formula for the velocity of the center of mass? A. v = αr B. v = ωr C. v = α/r D. v = ω/r E. v = ω 2 R

5 11. Students perform an experiment to determine the winner of a race. Three objects: an empty soup can, a solid cylindrical battery, and a marble roll without slipping down an inclined plane of vertical height H. In addition a box slides without friction another inclined plane with the same size. Based on the results of the experiment which object reaches the bottom the plane first? A. The can B. The battery C. The marble D. The box E. They all reach the bottom at the same time 12. Earth moves around the Sun in an elliptical orbit. The Earth approaches the closets point to the Sun its linear velocity increases. Which of the following doesn t change during the Earth s motion? A. The orbital radius B. The kinetic energy C. The potential energy D. The angular momentum E. More information is required 13. An ice skater performs a fast spin by pulling outstretched arms down and close to her body. What happens to her angular momentum with respect to the axis of rotation? A. It increases B. It decreases C. It doesn t change D. It depends how fast she rotates E. More information is required

6 14. An ice skater performs a fast spin by pulling outstretched arms down and close to her body. What happens to her kinetic energy with respect to the axis of rotation? A. It increases B. It decreases C. It doesn t change D. It depends how fast she rotates E. More information is required 15. Two boxes with masses 3 kg and 7 kg are attached the ends of a 1 m long lever. At which of the following points the lever should be placed on a fulcrum in order to keep the lever at equilibrium? A. A B. B C. C D. D E. E 16) A sphere and a cylinder of equal mass and radius are simultaneously released from rest on the same inclined plane and roll without sliding down the incline. Then: 1) the sphere reaches the bottom first because it has the greater inertia 2) the cylinder reaches the bottom first because it picks up more rotational energy 3) the sphere reaches the bottom first because it picks up more rotational energy 4) they reach the bottom together 5) none of the above are true

7 17) Two cylinders of the same size and mass roll down an incline. Cylinder A has most of its weight concentrated at the rim, while cylinder B has most of its weight concentrated at the center. Which reaches the bottom of the incline first? 1) A 2) B 3) Tie 18) Disks A and B are identical and roll across a floor with equal speeds. Then disk A rolls up an incline, reaching a maximum height h, and disk B moves up an incline that is identical except that it is frictionless. Is the maximum height reached by disk B greater than, less than, or equal to h? 1) greater than 2) less than 3) equal to 19) A hoop and a disk, each with the same mass M and same radius R, race down a hill. Who wins? (Assume they roll without slipping, and neglect rolling friction) 1) Hoop wins 2) Disk wins 3) Tie

8 20) A sphere, a hoop, and a cylinder, all with the same mass M and same radius R, are rolling along, all with the same speed v. Sphere Hoop Disk v v v Which has the most kinetic energy? 1) Sphere 2) Hoop 3) Disk 4) All have the same KE. 21) A thin-walled hollow tube rolls without sliding along the floor. The ratio of its translational kinetic energy to its rotational kinetic energy (about an axis through its center of mass) is: 1) 1 2) 2 3) 3 4) 1/2 5) 1/3 22) The second hand on a clock completes one revolution each minute. What is the direction of the angular momentum of the second hand as it passes the 12 at the top of the clock? 1) toward the 12 2) toward the 3 3) toward the 6 4) outward from the face of the clock 5) into the face of the clock

9 23) A uniform sphere of radius R rotates about a diameter with an angular momentum of magnitude L. Under the action of internal forces the sphere collapses to a uniform sphere of radius R/2. The magnitude of its new angular momentum is: 1) L/4 2) L/2 3) L 4) 2L 5) 4L 24) A child stands on the edge of a merry-go-round, which spins without friction. The child slowly walks towards the center of the platform. As the child moves toward the center, the platform's rotation rate: 1) Increases 2) Decreases 3) Stays the same 25) A star is rotating with a period T. Over a period of a million years, its radius decreases by a factor of 2. What is the new period of the star? 1) T/2 2) 2T 3) 4T 4) T/4 5) None of these. 26) A figure skater stands on one spot on the ice (assumed frictionless) and spins around with her arms extended. When she pulls in her arms, she reduces her rotational inertia and her angular speed increases so that her angular momentum is conserved. Compared to her initial rotational kinetic energy, her rotational kinetic energy after she has pulled in her arms must be 1) the same. 2) larger because she s rotating faster. 3) smaller because her rotational inertia is smaller.

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