Chapter 8: Rotational Motion of Solid Objects

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1 Chapter 8: Rotational Motion of Solid Objects 1. An isolated object is initially spinning at a constant speed. Then, although no external forces act upon it, its rotational speed increases. This must be due to A. an increase in the moment of inertia. B. an increase in the mass. C. an increase in the angular momentum. D. a decrease in the moment of inertia. E. impossible, angular momentum conservation is violated. 2. The bigger gears on the rear wheel of a multi-speed bike allow the rider to A. exert more force on the wheel. B. exert more torque on the wheel. C. increase the moment of inertia of the wheel. D. decrease the moment of inertia of the wheel. 3. Three horses are side-by-side on a merry-go-round: one at the edge, one near the axis, and one in between. Each horse has the same angular speed. Which horse has the greatest linear speed? A. The horse nearest the axis. B. The horse in the middle C. The horse at the edge. D. The linear speed is the same for all three horses. 4. A sphere and a hoop have the same diameter and the same mass. If they are released from rest at the top of an incline, which will reach the bottom more quickly? A. The sphere. B. The hoop. C. Both will require the same time to reach the bottom. 5. A torque acting on a body tends to produce A. equilibrium. B. linear velocity. C. a new center of gravity. D. angular rotation.

2 6. The angular momentum of an isolated object can be changed only by A. changing its rotational inertia. B. applying a force along the axis of rotation. C. applying a torque. 7. The rotational inertia of an object depends on which of these? A. Its color. B. How fast it is spinning. C. The amount of torque applied to it. D. How its mass is distributed about the spin axis. E. None of the above. 8. A football thrown with a spinning motion is more stable than one thrown without spin because A. its angular momentum is conserved. B. it is easier to part the air if it is spinning. C. gravity ignores spinning objects. D. the torque generated by the spinning action is conserved. 9. An object is moving in a horizontal circle, in a clockwise direction (as seen from above). In which direction does its angular momentum vector point? A. down B. up C. to the left D. toward the center of the circle 10. Using a longer handled wrench to loosen a tight nut allows you to A. exert more force on the nut. B. increase the moment of inertia of the nut. C. apply more torque to the nut. D. pull harder on the wrench. 11. A figure skater is spinning with her arms extended. She now pulls her arms close to her body. What happens? A. Her angular momentum increases. B. Her angular momentum decreases. C. Her moment of inertia increases. D. Her moment of inertia decreases.

3 12. A dancer begins performing a pirouette with arms extended. (A pirouette is a complete spin about a vertical axis.) This motion is completed most easily when the rotational inertia is decreased by A. ending at the waist at a right angle. B. extending the arms and one leg straight out to the sides. C. holding the arms straight up and extending one foot straight out to the side. D. bringing the arms and legs in a line with the body. 13. Because the rotational inertia is higher, it is hardest in springboard diving to perform a forward somersault in A. the straight position (no bending at knees or waist). B. the pike position (bending at the waist but not the knees). C. the tuck position (bending at both the waist and knees). 14. When a bicycle pedal is at the top of its motion, you can exert the greatest torque on the crank by A. pushing straight down on the pedal with your foot. B. pushing straight forward on the pedal with your foot. C. hooking your toes under the pedal and pulling upward. 15. A solid disk and a hollow disk are released together (from rest) to roll down an incline. They have the same diameter and mass. A. The hollow disk will reach the bottom first. B. They will reach the bottom at the same time. C. The solid disk will reach the bottom first. 16. In a stable stack of identical boards at the edge of a table, the center of gravity of the top board A. must lie above the table. B. must lie above the next lower board. C. must lie above the bottom board. D. need not lie over anything. 17. You stand with your heels against a wall and bend ninety degrees forward at the waist. A. You are able to maintain your balance. B. You fall forward because of the momentum you gain when you move. C. You fall forward because your center of gravity moves ahead of your base of support. D. You fall forward because the muscles in your feet aren't strong enough to stop you.

4 18. A constant torque is applied to a flywheel. Which of the following mechanical quantities will be constant? A. rotational energy B. angular momentum C. rotational acceleration D. rotational velocity E. linear velocity of a particle on the rim 19. A flywheel is used to minimize changes in rotational velocity as the torque or the load changes. The rotational inertia of a flywheel should be chosen to be A. as small as possible. B. as large as possible. C. anything -- it doesn't matter. 20. Three different bodies - a uniform sphere, a uniform disk, and a hoop - all have same radius and same mass. The body with the largest rotational inertia will be A. the hoop. B. the sphere. C. the disk. D. none, as all have the same value of rotational inertia. 21. In using a long steel rod as a lever to move a large rock, where should the fulcrum be placed? A. Halfway between the rock and the applied force. B. Close to the rock. C. Close the point where the force is applied. D. Anywhere in between - it makes no difference. 22. The angular momentum of a rotating body is conserved when A. no net force acts on the body. B. no net torque acts on the body. C. when the body has a constant angular acceleration. D. when a shape of the body does not change. 23. When an ice skater twirling on the point of a skate draws her arms in she ends up whirling faster. This is because A. rotational energy is conserved. B. angular momentum is conserved. C. linear momentum is conserved. D. a net torque acts on the skater.

5 24. A gyroscope consists of a wheel mounted on an axle aligned along a north-south direction. The south end of the axle is suspended by a rope attached to the ceiling, and the north end is manually held at rest. The wheel is spinning rapidly, so that its angular momentum vector points north. Suddenly the north end is released. Since there is spin, the north end of the axle will begin to move A. north. B. west. C. down. D. east. E. south. 25. The rotational velocity of a 45 rev/min phonograph record in rad/s is approximately: A. 45 rad/s. B. 283 rad/s. C rad/s. D. 4.7 rad/s. E rad/s. 26. The armature of a motor is accelerated uniformly from rest to a rotational velocity of 1800 rev/min in 10 seconds. The rotational acceleration of the motor is A. 180 rad/s 2. B. 90 rad/s 2. C rad/s 2. D rad/s 2. E. zero. 27. Which of the following is an appropriate unit for describing rotational acceleration? A. m/s 2. B. rad/min. C. rev/min. D. rev/m/s. E. rev/min 2. Answer: E 28. A wheel is spinning on an axle. The linear velocity of a point on the rim is the product of the radius times the rotational velocity, if the latter is measured in units of: A. deg/s. B. rev/s. C. rev/min. D. rad/s. E. deg/min.

6 29. Torque in the metric system is measured in units of: A. N. B. Ns. C. Nrad. D. N/m. E. Nm. Answer: E 30. A body of rotational inertia 1.0 kg m 2 is acted upon by a torque of 2.0 Nm. The angular acceleration of the body will be: A. 0.5 rad/s 2. B. 0.5 rev/s 2. C. 1.0 rad/s 2. D. 2.0 rad/s 2. E. 2.0 rev/s A merry-go-round, having a radius of 2.0 m, is set in motion by students applying a force of 500 N tangential to the rim of the wheel. The merry-go-round reaches a rotational velocity of 2.0 rad/s after 10 seconds, starting from rest. The rotational inertia of the merry-go-round is A. 1.0 x 10 5 kg m 2 B. 5.0 x 10 3 kg m 2 C. 5.0 x 10 4 kg m 2 D. 5.0 x 10 5 kg m 2 E. 1.0 x 10 4 kg m A student plays on a see-saw with her father. The student has a weight of 250 N and is seated 2.4 m from the axis of rotation. Her father balances her when he is seated 0.8 m from the axis. The father's weight is: A. 250 N. B. 500 N. C. 667 N. D. 725 N. E. 750 N. Answer: E 33. A solid disk and a hoop have different diameters and different masses. If they are released from rest at the top of an incline, which will reach the bottom more quickly? A. The solid disk. B. The hoop. C. Both will reach the bottom at the same time. D. Impossible to say without knowing which object has larger diameter. E. Impossible to say without knowing which object has larger mass.

7 34. A bicycle exhibits greater stability when the angular momentum of the wheels is A. smaller. B. larger. C. any value. 35. If the net force on a body is zero, the net torque on the body is A. always zero. B. not necessarily zero. C. certainly not zero. 36. If the net torque on a body is zero, the net force on the body is A. always zero. B. not necessarily zero. C. certainly not zero. 37. Just as torque is the rotational analogue of force in linear motion, rotational inertia is the rotational analogue of in linear motion. Answer: mass 38. When a mechanic uses an extension arm on his wrench to loosen a stubborn nut, he is exerting additional torque because of an increase in the (two words) of the force. Answer: lever arm 39. The angular momentum of a rotating body is constant when the net on the body is zero. Answer: torque 40. A merry-go-round is set into motion with a child on board. The rotational speed of the merry-go-round as the child moves outward along a radius. Answer: decreases 41. If the net force on a body is zero the net torque is (always, not necessarily, cannot be) zero. Answer: not necessarily 42. Consider the human forearm as a lever with the elbow the fulcrum. When a body of a given weight is held in the hand the force exerted by the muscles on the arm is than the weight. Answer: greater

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