Student AP Physics B Date Torque & Conservation of Angular Momentum 1. Complete the following statement: When a net torque is applied to a rigid object, it always produces a A) constant acceleration. B) rotational equilibrium. C) constant angular velocity. D) constant angular momentum. E) change in angular velocity. 2. A wrench is used to tighten a nut as shown in the figure. A 12-N force is applied 7.0 cm from the axis of rotation. What is the magnitude of the torque due to the applied force? A) 0.58 N m B) 0.84 N m C) 1.71 N m D) 14 N m E) 58 N m Page 1
3. A string is tied to a doorknob 0.72 m from the hinge as illustrated in the figure. At the instant shown, the force applied to the string is 5.0 N. What is the magnitude of the torque on the door? A) 2.1 N m B) 3.0 N m C) 1.0 N m D) 0.78 N m E) 0.60 N m 4. A uniform 13-kg trap door is oriented horizontally and hinged as shown. What is the magnitude of the torque on the door at the instant that the release is activated and the door can freely rotate? A) 4.9 N m B) 9.8 N m C) 48 N m D) 72 N m E) 96 N m 5. Complete the following statement: A body is in translational equilibrium A) only if it is at rest. B) only if it is moving with constant velocity. C) only if it is moving with constant acceleration. D) if it is either at rest or moving with constant velocity. E) if it is moving with either constant velocity or constant acceleration. Page 2
6. A horizontal, 10-m plank weighs 100 N. It rests on two supports that are placed 1.0 m from each end as shown in the figure. How close to one end can an 800-N person stand without causing the plank to tip? A) 0 m B) 0.3 m C) 0.5 m D) 0.7 m E) 0.9 m 7. A 3.0-kg ball and a 1.0-kg ball are placed at opposite ends of a massless beam so that the system is in equilibrium as shown. Note: The drawing is not drawn to scale. What is the value of the ratio of the lengths, b/a? A) 2.0 B) 2.5 C) 3.0 D) 4.0 E) 5.0 Page 3
8. One end of a rope is tied to the handle of a horizontally-oriented and uniform door. A force F is applied to the other end of the rope as shown in the drawing. The door has a weight of 145 N and is hinged on the right. What is the maximum magnitude of F for which the door will remain at rest? A) 145 N B) 265 N C) 381 N D) 424 N E) 530 N 9. A meter stick is pivoted at the 0.50-m line. A 3.0-kg object is hung from the 0.15-m line. Where should a 5.0-kg object be hung to achieve equilibrium (the meter stick oriented horizontal and motionless)? A) 0.06-m line B) 0.24-m line C) 0.56-m line D) 0.71-m line E) A 5.0-kg object cannot be placed anywhere on the meter stick to result in equilibrium in this system. Page 4
10. In the drawing shown, the large wheel has a radius of 7.1 m. A rope is wrapped around the edge of the wheel and a 7.6 kg-box hangs from the rope. A smaller disk of radius 1.38 m is attached to the wheel. A rope is wrapped around the edge of the disk as shown. An axis of rotation passes through the center of the wheel-disk system. What is the value of the mass M that will prevent the wheel from rotating? A) 34 kg B) 12 kg C) 17 kg D) 39 kg E) 46 kg Use the following to answer questions 11-12: An 80-kg man balances the boy on a teeter-totter as shown. Note: Ignore the weight of the board. Page 5
11. What is the approximate mass of the boy? A) 10 kg B) 20 kg C) 40 kg D) 45 kg E) 50 kg 12. What, approximately, is the magnitude of the downward force exerted on the fulcrum? A) zero newtons B) 100 N C) 600 N D) 800 N E) 1000 N 13. Which one of the following statements most accurately describes the center of gravity of an object? A) It is the point where gravity acts on the object. B) It is the point where all the mass is concentrated. C) It must be experimentally determined for all objects. D) It is the point on the object where all the weight is concentrated. E) It is the point from which the torque produced by the weight of the object can be calculated. 14. Consider four point masses located as shown in the sketch. The acceleration due to gravity is the same everywhere. What is the x coordinate of the center of gravity for this system? A) 2.0 m B) 2.7 m C) 3.0 m D) 3.3 m E) 3.8 m Page 6
15. Three objects are positioned along the x axis as follows: 4.4 kg at x = + 1.1 m, 3.7 kg at x = 0.80 m, and 2.9 kg at x = 1.6 m. The acceleration due to gravity is the same everywhere. What is the distance from the location of the center of gravity to the location of the center of mass for this system? A) zero meters B) 0.52 m C) 0.26 m D) +0.26 m E) +0.52 m 16. A 14-kg beam is hinged at one end. A 6.0-kg triangular object and a 7.5-kg I-shaped object are positioned as shown. Dots indicate the individual centers of gravity of the beam and the two objects. What is the distance from the axis of rotation to the center of gravity for this system? A) 1.3 m B) 1.1 m C) 0.96 m D) 0.89 m E) 0.71 m Page 7
17. A massless frame in the shape of a square with 2-m sides has a 1-kg ball at each corner. What is the moment of inertia of the four balls about an axis through the corner marked O and perpendicular to the plane of the paper? A) 4 kg m 2 B) 8 kg m 2 C) 10 kg m 2 D) 12 kg m 2 E) 16 kg m 2 18. The drawing shows the top view of a door that is 1.68 m wide. Two forces are applied to the door as indicated. What is the magnitude of the net torque on the door with respect to the hinge? A) 0 N m B) 4.4 N m C) 8.3 N m D) 9.1 N m E) 11 N m Page 8
19. Three objects are attached to a massless rigid rod that has an axis of rotation as shown. Assuming all of the mass of each object is located at the point shown for each, calculate the moment of inertia of this system. A) 1.3 kg m 2 B) 3.1 kg m 2 C) 5.3 kg m 2 D) 7.2 kg m 2 E) 9.1 kg m 2 20. A solid sphere rolls without slipping along a horizontal surface. What percentage of its total kinetic energy is rotational kinetic energy? A) 33 % B) 50 % C) 12 % D) 75 % E) 29 % 21. A child standing on the edge of a freely spinning merry-go-round moves quickly to the center. Which one of the following statements is necessarily true concerning this event and why? A) The angular speed of the system decreases because the moment of inertia of the system has increased. B) The angular speed of the system increases because the moment of inertia of the system has increased. C) The angular speed of the system decreases because the moment of inertia of the system has decreased. D) The angular speed of the system increases because the moment of inertia of the system has decreased. E) The angular speed of the system remains the same because the net torque on the merry-go-round is zero N m. Page 9
22. What happens when a spinning ice skater draws in her outstretched arms? A) Her angular momentum decreases. B) Her angular momentum increases. C) Her moment of inertia decreases causing her to speed up. D) Her moment of inertia decreases causing her to slow down. E) The torque that she exerts increases her moment of inertia. 23. A spinning star begins to collapse under its own gravitational pull. Which one of the following occurs as the star becomes smaller? A) The star's angular velocity decreases. B) The star's angular momentum remains constant. C) The star's angular momentum increases. D) The star's angular velocity remains constant. E) Both the star's angular momentum and its angular velocity remain constant. 24. A spinning skater draws in her outstretched arms thereby reducing her moment of inertia by a factor of 2. Determine the ratio of her final kinetic energy to her initial kinetic energy. A) 0.5 B) 1 C) 2 D) 4 E) 16 25. A 60.0-kg skater begins a spin with an angular speed of 6.0 rad/s. By changing the position of her arms, the skater decreases her moment of inertia to one-half its initial value. What is the skater's final angular speed? A) 3.0 rad/s B) 4.5 rad/s C) 9.0 rad/s D) 12 rad/s E) 18 rad/s Page 10
Use the following to answer questions 26-27: Two skaters, each of mass 40 kg, approach each other along parallel paths that are separated by a distance of 2 m. Both skaters have a speed of 10 m/s. The first skater carries a 2-m pole that may be considered massless. As he passes the pole, the second skater catches hold of the end. The two skaters then go around in a circle about the center of the pole. 26. What is the angular speed of the skaters after they have linked together? A) 4 rad/s B) 5 rad/s C) 10 rad/s D) 20 rad/s E) 40 rad/s 27. What is their combined angular momentum about the center of the pole? A) 2 kg m 2 /s B) 40 kg m 2 /s C) 80 kg m 2 /s D) 400 kg m 2 /s E) 800 kg m 2 /s 28. A compact disc rotates about its center at constant angular speed. Which one of the following quantities is constant and non-zero for a dust particle near the edge of the disc? A) linear velocity B) torque about the center of the disc C) centripetal acceleration D) angular momentum E) angular acceleration Page 11
Use the following to answer questions 29-30: A 2.0-kg hoop rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of 6.0 m/s. 2.0 kg 6 m/s 29. Which one of the following statements is true concerning the angular momentum of this hoop? A) It points into the paper. B) It points out of the paper. C) It points to the left. D) It points to the right. E) It varies from point to point on the hoop. 30. What is the total kinetic energy of the hoop? A) 36 J B) 54 J C) 72 J D) 96 J E) 140 J Page 12
Answer Key 1. E 2. B 3. B 4. C 5. D 6. C 7. D 8. B 9. D 10. D 11. B 12. E 13. E 14. C 15. A 16. A 17. E 18. C 19. E 20. E 21. D 22. C 23. B 24. C 25. D 26. C 27. E 28. D 29. A 30. C Page 13