A bucket of water with total mass 26 kg is attached to a rope, which in turn is wound around a 0.04-m radius cylinder at the top of a well. A crank with a turning radius of 0.20 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.11 kgm2 . If the bucket is raised to the top of the well and released, what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope's mass is negligible, that cylinder turns on frictionless bearings and that g = 9.8 m/s2.)
a. 1.9 m/s2 b. 2.7 m/s2
c. 9.8 m/s2 d. 7.9 m/s2
e. 7.1 m/s2
[Ques. 2] A baseball pitcher loosens up his pitching arm. He tosses a 0.140-kg ball using only the rotation of his forearm, 0.270 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 24.0 m/s in a time of 0.425 s, what torque is applied to the ball while being held by the pitcher's hand to produce the angular acceleration?
a. 29.3 Nm b. 21.3 Nm
c. 2.13 Nm d. 2.93 Nm
e. 209 Nm
[Ques. 3] A baseball pitcher, loosening up his arm before a game, tosses a 0.140-kg ball using only the rotation of his forearm, 0.290 m in length, to accelerate the ball. If the ball starts at rest and is released with a speed of 24.0 m/s in a time of 0.450 s, what is the average angular acceleration of the arm and ball?
a. 3.13 rad/s2 b. 37.2 rad/s2
c. 15.5 rad/s2 d. 184 rad/s2
e. 25.7 rad/s2
[Ques. 4] A disk has a moment of inertia of 3.0 104 kgm2 and rotates with an angular speed of 3.6 rad/s. What net torque must be applied to bring it to rest within 3.6 s?
a. 3.89E4 Nm b. 3.00E4 Nm
c. 4.32E4 Nm d. 3.00E4 Nm
e. 1.20E4 Nm
[Ques. 5] A ventilation fan with a moment of inertia of 0.040 kgm2 has a net torque of 0.160 Nm applied to it. What angular acceleration does it experience?
a. 0.0064 rad/s2 b. 4.0 rad/s2
c. 0.25 rad/s2 d. 0.40 rad/s2
e. 0.20 rad/s2
[Ques. 6] If a nonzero torque is applied to an object, that object will experience:
a. a constant angular speed. b. an angular acceleration.
c. a constant moment of inertia. d. an increasing moment of inertia.
[Ques. 7] A non-uniform rod of length L and mass M is pivoted about one end. The moment of inertia of this rod about its pivoted end is 1ML2/4 . Attached to the rod is a mass 3M at its midpoint and at the end opposite the pivot is another mass 2M. What is the moment of inertia of this configuration about the pivot?
a. 3ML2 b. 2ML2
c. 4ML2 d. 5ML2
e. None of the above answers is correct.
[Ques. 8] A uniform rod of length L and mass M is pivoted about one end. Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass M. What is the moment of inertia of this configuration about the pivot?
a. 3ML2 b. 7ML2/12
c. 4ML2/3 d. 19ML2/12
[Ques. 9] An object consists of a rod (of length 3.00 m and negligible moment of inertia) to which four small 3.50-kg masses are attached, one at each end and one at each point on the rod spaced at 1.00-m intervals. The moment of inertia of this object about an axis perpendicular to the rod and through one of the end masses:
a. is 49 kgm2.
b. is 21 kgm2.
c. is 31.5 kgm2.
d. is 10.5 kgm2.
e. cannot be uniquely determined until it is stated which inner mass the axis goes through.
[Ques. 10] Two hoops or rings (I = MR2) are centered, lying on a turntable. The smaller ring has radius = 0.05 m; the larger has radius = 0.10 m. Both have a mass of 5.0 kg. What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.
a. 7.5E1 kgm2 b. 1.1E1 kgm2
c. 1.3E2 kgm2 d. 6.3E2 kgm2
e. 5.0E2 kgm2
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