A rotating flywheel can be used as a method to store energy. If it has 2.00 106 J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.00 N m acts on the system, in what interval of time would the flywheel come to rest?
a. 2 500 min b. 41.7 min
c. 25.0 min d. 167 min
[Ques. 2] 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 2.00 106 J when rotating at 400 rad/s, what moment of inertia is required?
a. 50.0 kg m2 b. 25.0 kg m2
c. 12.5 kg m2 d. 6.30 kg m2
[Ques. 3] A hoop 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 hoop, I = MR2.)
a. 1/4 b. 1/2
c. 1/1 d. 2/5
[Ques. 4] A cylinder with its mass concentrated toward the center has a moment of inertia of 0.2MR2 . 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?
a. 1/l0 b. 1/5
c. 1/2 d. 1/1
[Ques. 5] A bucket of water with total mass 21.0 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 0.21 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 5.4 m/s?
a. 4.8E+2 J b. 1.2E+3 J
c. 3.1E+2 J d. 1.2E+4 J
[Ques. 6] A bowling ball has a mass of 7.00 kg, a moment of inertia of 2.80 102 kgm2, and a radius of 0.100 m. If it rolls down the lane without slipping at a linear speed of 4.00 m/s, what is its total kinetic energy?
a. 78.4 J b. 22.4 J
c. 56.0 J d. 40.0 J
[Ques. 7] A ventilation fan with a moment of inertia of 0.0340 kgm2 has a net torque of 0.110 N m applied to it. If it starts from rest, what kinetic energy will it have 10.4 s later?
a. 1.84 J b. 19.2 J
c. 33.6 J d. 38.5 J
[Ques. 8] A bucket of water with total mass 20.0 kg is attached to a rope, which in turn is wound around a 4.00-cm radius cylinder at the top of a well. The bucket is raised to the top of the well and released. The bucket is moving with a speed of 8.00 m/s upon hitting the water surface in the well. What is the angular speed of the cylinder at this instant?
a. 64.0 rad/s b. 50.3 rad/s
c. 200 rad/s d. 126 rad/s
e. 393 rad/s
[Ques. 9] A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.250 m/s?
a. 5.00 rev/s b. 7.85 rev/s
c. 1.59 rev/s d. 0.80 rev/s
e. 3.18 rev/s
[Ques. 10] A rod of length L is hinged at one end. The moment of inertia as the rod rotates around that hinge is ML2/3 . Suppose a 2.00-m rod with a mass of 6.00 kg is hinged at one end and is held in a horizontal position. The rod is released as the free end is allowed to fall. What is the angular acceleration as it is released?
a. 1.09 rad/s2 b. 4.50 rad/s2
c. 7.35 rad/s2 d. 0.82 rad/s2
e. 4.90 rad/s2
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