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44. A ventilation fan with a moment of inertia of 0.034 kg˜m2 _{has a net torque of 0.11 N˜m}

applied to it. If it starts from rest, what kinetic energy will it have 8.0 s later? a. 31 J

b. 17 J c. 11 J d. 6.6 J

45. The total kinetic energy of a baseball thrown with a spinning motion is a function of: a. its linear speed but not rotational speed.

b. its rotational speed but not linear speed. c. both linear and rotational speeds. d. neither linear nor rotational speed.

46. A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 u 102 _kg˜m2 _{and a radius of}

0.10 m. If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its total kinetic energy?

a. 45 J b. 32 J c. 11 J d. 78 J

47. A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well. The moment of inertia of the cylinder and crank is 0.12 kg˜m2_{. The bucket is raised to the top of the well and released to}

fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 8.0 m/s?

a. 2.1 u 103 _J

b. 1.5 u 103 _J

c. 0.70 u 103 _J

d. 0.40 u 103 _J

48. A solid sphere of mass 4.0 kg and radius 0.12 m is at rest at the top of a ramp inclined 15q. It rolls to the bottom without slipping. The upper end of the ramp is 1.2 m higher than the lower end. Find the sphere’s total kinetic energy when it reaches the bottom.

a. 70 J b. 47 J c. 18 J d. 8.8 J

49. A solid sphere of mass 4.0 kg and radius 0.12 m starts from rest at the top of a ramp inclined 15q, and rolls to the bottom. The upper end of the ramp is 1.2 m higher than the lower end. What is the linear speed of the sphere when it reaches the bottom of the ramp? (Note: > = 0.4?+2 _{for a solid sphere and ; = 9.8 m/s}2₎

a. 4.7 m/s b. 4.1 m/s c. 3.4 m/s d. 2.4 m/s

50. A solid cylinder of mass 3.0 kg and radius 0.2 m starts from rest at the top of a ramp, inclined 15q, and rolls to the bottom without slipping. (For a cylinder > = 0.5?+2_{) The upper end of}

the ramp is 1.2 m higher than the lower end. Find the linear speed of the cylinder when it reaches the bottom of the ramp. (; = 9.8 m/s2₎

a. 4.7 m/s b. 4.3 m/s c. 4.0 m/s d. 2.4 m/s

51. A gyroscope has a moment of inertia of 0.14 kg˜m2 _{and an initial angular speed of 15 rad/s.}

Friction in the bearings causes its speed to reduce to zero in 30 s. What is the value of the average frictional torque?

a. 3.3 u 102 _N˜m

b. 8.1 u 102 _N˜m

c. 14 u 102 _N˜m

d. 7.0 u 102 _N˜m

52. A gyroscope has a moment of inertia of 0.140 kg˜m2 _{and has an initial angular speed of 15.0}

rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 u 102 _{N˜m, then in what time interval will the gyroscope coast from 15.0}

rad/s to zero? a. 150 s b. 105 s c. 90.0 s d. 180 s

53. A cylinder with its mass concentrated toward the center has a moment of inertia of 0.1 ?+2_.

If this cylinder is rolling without slipping along a level surface with a linear speed !, what is

the ratio of its rotational kinetic energy to its linear kinetic energy? a. 1/l0

b. 1/5 c. 1/2 d. 1/1

54. A solid sphere with mass, ?, and radius, +, rolls along a level surface without slipping with a linear speed, !. What is the ratio of rotational to linear kinetic energy? (For a solid sphere, > =

0.4 ?+2_). a. 1/4 b. 1/2 c. 1/1 d. 2/5

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55. A rotating flywheel can be used as a method to store energy. If it is required that such a device be able to store up to a maximum of 1.00 u 106 _{J when rotating at 400 rad/s, what}

moment of inertia is required? a. 50 kg˜m2

b. 25 kg˜m2

c. 12.5 kg˜m2

d. 6.3 kg˜m2

56. A rotating flywheel can be used as a method to store energy. If it has 1.0 u 106 _{J of kinetic}

energy when rotating at 400 rad/s, and if a frictional torque of 4.0 N˜m acts on the system, in what interval of time would the flywheel come to rest?

a. 3.5 min b. 7.0 min c. 14 min d. 21 min

57. An initially installed flywheel can store 106 _{J of kinetic energy when rotating at 300 rad/s. It}

is replaced by another flywheel of the same size but made of a lighter and stronger material. If its mass is half that of the original and it is now capable of achieving a rotational speed of 600 rad/s, what maximum energy can be stored?

a. 40 u 105 _J

b. 20 u 105 _J

c. 10 u 105 _J

d. 5.0 u 105 _J

58. A cylinder (> = ?+2_{/2) is rolling along the ground at 7.0 m/s. It comes to a hill and starts}

going up. Assuming no losses to friction, how high does it get before it stops? a. 1.2 m

b. 3.7 m c. 4.2 m d. 5.9 m

59. A meter stick is hinged at its lower end and allowed to fall from a vertical position. If its moment of inertia is ?@2_{/3, with what angular speed does it hit the table?}

a. 5.42 rad/s b. 2.71 rad/s c. 1.22 rad/s d. 7.67 rad/s

60. A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3 000 rpm) by an electric motor. The flywheel is a solid cylinder of mass 500 kg and radius 0.500 m (>cylinder = ?+2/2). If the bus requires an average power of 10.0

kW, how long will the flywheel rotate? a. 154 s

b. 308 s c. 463 s d. 617 s

61. An object of radius R and moment of inertia I rolls down an incline of height H after starting from rest. Its total kinetic energy at the bottom of the incline:

a. is gR/I. b. is I/gH. c. is 0.5 Ig/H.

d. cannot be found from the given information alone.

62. A uniform solid sphere rolls down an incline of height 3 m after starting from rest. In order to calculate its speed at the bottom of the incline, one needs to know:

a. the mass of the sphere. b. the radius of the sphere.

c. the mass and the radius of the sphere. d. no more than is given in the problem.

63. Consider the use of the terms “rotation” and “revolution”. In physics: a. the words are used interchangeably.

b. the words are used interchangeably but “rotation” is the preferred word. c. the words have different meaning.

d. “rotation” is the correct word and “revolution” should not be used.

64. A solid disk of radius R rolls down an incline in time T. The center of the disk is removed up to a radius of R/2. The remaining portion of the disk with its center gone is again rolled down the same incline. The time it takes is:

a. T.

b. more than T. c. less than T.

d. requires more information than given in the problem to figure out.