## Mechanical Rotation Design Multiple Choice Questions

1. A disk starts from rest and rotates about a fixed axis, subject to a constant net torque. The work done by the torque during the second revolution is _________ as the work done during the first revolution.

A. The same

B. Twice as much

C. Half as much

D. Four times as much

2. A wheel rotates with a constant angular acceleration of π rad/s². During the time interval from t1 to t2 its angular displacement is π rad. At time t2 its angular velocity is 2π rad/sec. Its angular velocity in rad/s at time t1 is:

A. Zero

B. 1

C. π

D. π/√2

3. ‘A’ and ‘B’ are two solid cylinders made of aluminum. Their dimensions are shown. The ratio of the rotational inertia of B to that of ‘A’ about the common axis X-X’ is:

A. 2

B. 4

C. 8

D. 32

4. A wheel initially has an angular velocity of -36 rad/sec but after 6.0 sec its angular velocity is -24 rad/sec. If its angular acceleration is constant the value is:

5. A child, riding on a large merry-go-round, travels a distance of 3000 m in a circle of diameter 40 m. The total angle in radians through which she revolves is:

A. 50

B. 75

C. 150

D. None of these

6. For a wheel spinning on an axis through its center, the ratio of the tangential acceleration of a point on the rim to the tangential acceleration of a point halfway between the center and the rim is:

A. 1

B. 2

C. 1/2

D. 4

7. Three identical balls are tied by light strings to the same rod and rotate around it, as shown below. Rank the balls according to their rotational inertia, least to greatest.

A. 1, 2, 3

B. 3, 2, 1

C. 3, then 1 and 2 tie

D. 1, 3, 2

8. The rotational inertia of a disk about its axis is 0.70 kg.m2. When a 2.0 kg weight is added to its rim, 0.40 m from the axis, the rotational inertia becomes:

A. 0.38 kg.m2

B. 0.54 kg.m2

C. 0.70 kg.m2

D. 1.0 kg.m2

9. One revolution is about the same as:

10. A disk with a rotational inertia of 5.0 kg.m2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied tangentially to the rim. The angular acceleration of the disk is:

11. A 16 kg block is attached to a cord that is wrapped around the rim of a flywheel of diameter 0.40 m and hangs vertically, as shown. The rotational inertia of the flywheel is 0.50 kgm2. When the block is released and the cord unwinds, the acceleration of the block is:

A. 0.15 g

B. 0.56 g

C. 0.84 g

D. 100 g

12. A 8.0-cm radius disk with a rotational inertia of 0.12 kgm2 is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by using a crank to apply a 9.0-Nm torque to the disk. The acceleration of the mass is:

A. 0.50 m/s2

B. 1.7 m/s2

C. 6.2 m/s2

D. 12 m/s2

13. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 × 10-3 kgm2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. At any instant after the blocks start moving the object with the greatest kinetic energy is:

A. The heavier block

B. The lighter block

C. The pulley

D. Either block (the two blocks have the same kinetic energy)

14. If a wheel turns with constant angular speed then:

A. Each point on its rim moves with constant velocity

B. Each point on its rim moves with constant acceleration

C. The wheel turns through equal angles in equal times

D. The angle through which the wheel turns in each second increases as time goes on

15. A flywheel, initially at rest, has a constant angular acceleration. After 9 s the flywheel has rotated 450 rad. Its angular acceleration in rad/sec2 is:

A. 100

B. 1.77

C. 50

D. 11.1

16. Four identical particles, each with mass m, are arranged in the x, y plane as shown. They are connected by light sticks to form a rigid body. If m = 2.0 kg and a = 1.0 m, the rotational inertia of this array about the y-axis is:

A. 4.0 kg.m2

B. 12 kg.m2

C. 9.6 kg/m2

D. 4.8 kg/m2

17. Two circular disks having the same mass and the same thickness are made from different materials. The disk with the smaller rotational inertia is:

A. The one made from the more dense material

B. The one made from the less dense material

C. Neither — both rotational inertias are the same

D. The disk with the larger angular velocity

18. The meter stick shown below rotates about an axis through the point marked, 20 cm from one end. Five forces act on the stick: one at each end, one at the pivot point, and two 40 cm from one end, as shown. The magnitudes of the forces are all the same. Rank the forces according to the magnitudes of the torques they produce about the pivot point, least to greatest.

A. F1, F2, F3, F4, F5

B. F1 and F2 tie, then F3, F4, F5

C. F2 and F5 tie, then F4, F1, F3

D. F2 and F5 tie, then F4, then F1 and F3 tie

19. A cylinder is 0.10 m in radius and 0.20 in length. Its rotational inertia, about the cylinder axis on which it is mounted is 0.020 kg.m2. A string is wound around the cylinder and pulled with a force of 1.0 N. The angular acceleration of the cylinder is:

20. A certain wheel has a rotational inertia of 12 kgm2. As it turns through 5.0 rev its angular velocity increases from 5.0 rad/s to 6.0 rad/s. If the net torque is constant, its value is:

A. 0.016 Nm

B. 0.18 Nm

C. 0.57 Nm

D. 2.1 Nm

21. A small disk of radius R1 is fastened coaxially to a larger disk of radius R2. The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force F as shown. The tension in the string pulling the block is:

A. R1F/R2

B. mR1R2F/(I – mR22 )

C. mR1R2F/(I + mR22 )

D. mR1R2F/(I – mR1R2)

22. A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The work done by the torque during the second 5 s is __________ as the work done during the first 5s.

A. The same

B. Twice as much

C. Half as much

D. Four times as much

23. One revolution per minute is about:

24. If a wheel turning at a constant rate completes 100 revolutions in 10 sec its angular speed is:

25. A flywheel of diameter 1.2 m has a constant angular acceleration of 5.0 rad/s2. The tangential acceleration of a point on its rim is:

B. 3.0 m/s2

C. 5.0 m/s2

D. 6.0 m/s2

26. The rotational inertia of a wheel about its axle does not depend upon its:

A. Diameter

B. Mass

C. Distribution of mass

D. Speed of rotation

27. When a thin uniform stick of mass M and length L is pivoted about its midpoint, its rotational inertia is ML2/12. When pivoted about a parallel axis through one end, its rotational inertia is:

A. ML2/12

B. ML2/6

C. ML2/3

D. 7ML2/12

29. As a particle starts from rest and moves with constant angular acceleration around a circular orbit, the point of application of the force acting on it does not change. This must mean:

A. The torque acting on it is increasing in magnitude

B. The torque acting on it is decreasing in magnitude

C. The force acting on it is increasing in magnitude

D. The force acting on it is decreasing in magnitude

30. A thin circular hoop of mass 1.0 kg and radius 2.0 m is rotating about an axis through its center and perpendicular to its plane. It is slowing down at the rate of 7.0 rad/s2. The net torque acting on it is:

A. 7.0 Nm

B. 14.0 Nm

C. 28.0 Nm

D. 44.0 Nm

31. A wheel is spinning at 27 rad/sec but is slowing with an acceleration that has a magnitude given by 3t2, in rad/s² for t in seconds. It stops in a time of:

A. 1.7 s

B. 2.6 s

C. 3.0 s

D. 4.4 s

32. A disk with a rotational inertia of 5.0 kgm2 and a radius of 0.25 m rotates on a fixed axis perpendicular to the disk and through its center. A force of 2.0 N is applied tangentially to the rim. As the disk turns through half a revolution the work done by the force is:

A. 1.6 J

B. 2.5 J

C. 6.3 J

D. 10 J

33. The rotational inertia of a thin cylindrical shell of mass ‘M’, radius ‘R’, and length ‘L’ about its central axis (X – X’) is

A. MR2/2

B. ML2/2

C. ML2

D. MR2

34. The rotational inertia of a solid uniform sphere about a diameter is (2/5)MR2, where M is its mass and R is its radius. If the sphere is pivoted about an axis that is tangent to its surface, its rotational inertia is:

A. MR2

B. (2/5) MR2

C. (3/5) MR2

D. (7/5) MR2

35. A disk with a rotational inertia of 5.0 kg .m2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 2.0 N is applied parallel to the axis. The angular acceleration of the disk is:

A. 0

36. A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 × 10-3 kgm2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. When the velocity of the heavier block is 2.0 m/s the total kinetic energy of the pulley and blocks is:

A. 2.0 J

B. 4.0 J

C. 14 J

D. 22 J

37. String is wrapped around the periphery of a 5.0 cm radius cylinder, free to rotate on its axis. The string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder. As each small segment of string leaves the cylinder, its acceleration changes by:

A. 0.010 m/sec2

B. 0.020 m/sec2

C. 0.10 m/sec2

D. 0.20 m/sec2

38. If a wheel is turning at 3.0 rad/sec, the time it takes to complete one revolution is about:

A. 0.33 sec

B. 0.67 sec

C. 1.0 sec

D. 2.1 sec

39. A flywheel rotating at 12 rev/s is brought to rest in 6 sec. The magnitude of the average angular acceleration in rad/s2 of the wheel during this process is:

A. 1/π

B. 2

C. 4

D. 4π

40. Three identical objects, each of mass ‘M’, are fastened to a mass less rod of length ‘L’ as shown. The rotational inertia about one end of the rod of this array is:

A. ML2/2

B. ML2

C. 3ML2/2

D. 5ML2/4

41. To increase the rotational inertia of a solid disk about its axis without changing its mass:

A. Drill holes near the rim and put the material near the axis

B. Drill holes near the axis and put the material near the rim

C. Drill holes at points on a circle near the rim and put the material at points between the holes

D. Drill holes at points on a circle near the axis and put the material at points between the holes

42. A disk with a rotational inertia of 5.0 kg.m2 and a radius of 0.25 m rotates on a frictionless fixed axis perpendicular to the disk and through its center. A force of 8.0 N is applied tangentially to the rim. If the disk starts at rest, then after it has turned through half a revolution its angular velocity is:

43. A small disk of radius R1 is mounted coaxially with a larger disk of radius R2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless table top. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force F as shown. The acceleration of the block is:

A. R1F/mR2

B. R1R2F/(I – mR22 )

C. R1R2F/(I + mR22 )

D. R1R2F/(I – mR1R2)

44. A disk has a rotational inertia of 6.0 kgm2 and a constant angular acceleration of 2.0 rad/s². If it starts from rest the work done during the first 5.0 s by the net torque acting on it is:

A. 0

B. 30 J

C. 60 J

D. 300 J

45. The angular speed in rad/sec of the second hand of a watch is:

A. π/1800

B. π/60

C. π/30

D. 2π

46. A wheel starts from rest and has an angular acceleration of 4.0 rad/s². When it has made 10 rev its angular velocity is:

47. A wheel starts from rest and has an angular acceleration of 4.0 rad/s². The time it takes to make 10 revolutions is:

A. 0.50 sec

B. 0.71 sec

C. 2.2 sec

D. 5.6 sec

48. A rod is pivoted about its center. A 5-N force is applied 4 m from the pivot and another 5-N force is applied 2 m from the pivot, as shown. The magnitude of the total torque about the pivot (in N.m) is:

A. 0

B. 5

C. 8.7

D. 15

49. A car travels north at constant velocity. It goes over a piece of mud which sticks to the tire. The initial acceleration of the mud, as it leaves the ground, is:

A. Vertically upward

B. Horizontally to the north

C. Horizontally to the south

D. Zero

50. A 0.70-kg disk with a rotational inertia given by MR2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip then as the mass falls and the cylinder rotates the suspension holding the cylinder pulls up on the cylinder with a force of:

A. 6.9 N

B. 9.8 N

C. 16 N

D. 26 N

51. The angular speed in rad/sec of the minute hand of a watch is:

A. 60/π

B. 1800/π

C. π

D. π/1800

52. A wheel initially has an angular velocity of 18 rad/sec but it is slowing at a rate of 2.0 rad/s2. The time it takes to stop is:

A. 3.0 sec

B. 6.0 sec

C. 9.0 sec

D. 12 sec

53. The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then:

A. The body is slowing down

B. The body is speeding up

C. The body is starting to turn in the opposite direction

D. The axis of rotation is changing orientation

54. For a wheel spinning on an axis through its center, the ratio of the radial acceleration of a point on the rim to the radial acceleration of a point halfway between the center and the rim is:

A. 1

B. 2

C. 1/2

D. 4

55. Consider four objects, each having the same mass and the same radius:

1. A solid sphere

2. A hollow sphere

3. A flat disk in the x, y plane

4. A hoop in the x, y plane

The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is:

A. 1, 2, 3, 4

B. 4, 3, 2, 1

C. 1, 3, 2, 4

D. 4, 2, 3, 1

56. A disk is free to rotate on a fixed axis. A force of given magnitude F, in the plane of the disk, is to be applied. Of the following alternatives the greatest angular acceleration is obtained if the force is:

A. Applied tangentially halfway between the axis and the rim

B. Applied tangentially at the rim

C. Applied radially halfway between the axis and the rim

D. Applied radially at the rim

57. A phonograph turntable, rotating at 0.75 rev/sec, slows down and stops in 30 sec. The magnitude of its average angular acceleration in rad/s2 for this process is:

A. 1.5

B. 1.5π

C. π/40

D. π/20

57. If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning:

A. Clockwise about an axis that is perpendicular to the page

B. Counterclockwise about an axis that is perpendicular to the page

C. About an axis that is parallel to the page

D. About an axis that is changing orientation

58. 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 of a point halfway between the center and the rim is:

A. 1

B. 2

C. 1/2

D. 4

59. A solid cylinder made of lead has the same mass and the same length as a solid cylinder made of wood. The rotational inertia of the lead cylinder compared to the wooden one is:

A. Greater

B. Less

C. Same

D. Unknown unless the radii are given

60. A block is attached to each end of a rope that passes over a pulley suspended from the ceiling. The blocks do not have the same mass. If the rope does not slip on the pulley, then at any instant after the blocks start moving the rope:

A. Pulls on both blocks, but exerts a greater force on the heavier block

B. Pulls on both blocks, but exerts a greater force on the lighter block

C. Pulls on both blocks and exerts the same non-zero force on both

D. Does not pull on either block

61. A uniform disk, a thin hoop, and a uniform sphere, all with the same mass and same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are simultaneously applied to the rims, as shown. Rank the objects according to their angular velocities after a given time t, least to greatest.

A. Disk, hoop, sphere

B. Hoop, disk, sphere

C. Hoop, sphere, disk

D. Hoop, disk, sphere

62. A wheel starts from rest and spins with a constant angular acceleration. As time goes on the acceleration vector for a point on the rim:

A. Decreases in magnitude and becomes more nearly tangent to the rim

B. Decreases in magnitude and becomes more nearly radial

C. Increases in magnitude and becomes more nearly tangent to the rim

D. Increases in magnitude and becomes more nearly radial

63. The angular velocity of a rotating wheel increases 2 rev/s every minute. The angular acceleration, in rad/s2 of this wheel is:

A. 4π/2

B. 2π

C. 1/30

D. 2π/30

64. A wheel initially has an angular velocity of 36 rad/sec but after 6.0sec its angular velocity is 24 rad/sec. If its angular acceleration is constant the value is:

65. A wheel initially has an angular velocity of 18 rad/sec but it is slowing at a rate of 2.0 rad/s². By the time it stops it will have turned through:

A. 13 rev

B. 26 rev

C. 39 rev

D. 52 rev

66. A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s². The cord will unwind in:

A. 0.82 sec

B. 2.0 sec

C. 8.0 sec

D. 16 sec

67. Two wheels are identical but wheel ‘B’ is spinning with twice the angular velocity of wheel ‘A’. The ratio of the radial acceleration of a point on the rim of ‘B’ to the radial acceleration of a point on the rim of ‘A’ is:

A. 1

B. 2

C. 1/2

D. 4

68. Ten seconds after an electric fan is turned on, the fan rotates at 300 rev/min. Its average angular acceleration is:

C. 30 rev/sec2

D. 50 rev/min2

69. The acceleration of a point on a spinning wheel is increased by a factor of 4 if:

A. The angular velocity and the angular acceleration are each increased by a factor of 4

B. The angular velocity is increased by a factor of 4 and the angular acceleration is not changed

C. The angular velocity and the angular acceleration are each increased by a factor of 2

D. The angular velocity is increased by a factor of 2 and the angular acceleration is increased by a factor of 4

70. A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5) MR2. A light string of length 2R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is:

A. (2/5) MR²

B. 4 MR2

C. (7/5) MR2

D. (47/5) MR2

71. A force with a given magnitude is to be applied to a wheel. The torque can be maximized by:

A. Applying the force near the axle, radially outward from the axle

B. Applying the force near the rim, radially outward from the axle

C. Applying the force near the axle, parallel to a tangent to the wheel

D. Applying the force at the rim, tangent to the rim

72. A grinding wheel, used to sharpen tools, is powered by a motor. A knife held against the wheel exerts a torque of 0.80 Nm. If the wheel rotates with a constant angular velocity of 20 rad/s the work done on the wheel by the motor in 1.0 min is:

A. 0

B. 480 J

C. 960 J

D. 1400 J

73. String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. If the string is pulled out at a constant rate of 10 cm/sec and does not slip on the cylinder, the angular velocity of the cylinder is: