56. A cylinder with its mass concentrated toward the center : 2102161
56. A cylinder with its mass concentrated toward the center has a moment of inertia of 0.1 MR2. If this cylinder is rolling without slipping along a level surface with a linear speed v, what is the ratio of its rotational kinetic energy to its linear kinetic energy?
57. A solid sphere with mass, M, and radius, R, rolls along a level surface without slipping with a linear speed, v. What is the ratio of rotational to linear kinetic energy? (For a solid sphere, I = 0.4 MR2)
58. 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 ´ 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
59. A rotating flywheel can be used as a method to store energy. If it has 1.0 ´ 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
60. 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 ´ 105 J
B. 20 ´ 105 J
C. 10 ´ 105 J
D. 5.0 ´ 105 J