Chapter 11: Rotational Dynamics and Static Equilibrium Selected Solutions

Selected Solutions

11. (a) For a disk, . We can use the work-energy theorem to determine the average torque.

Therefore,

Doubling the mass and halving the radius reduces I by a factor of 2 and therefore reduces the wheel's kinetic energy. The same torque brings the wheel to rest in a decreased angle of rotation.

27. (a) The rod is in equilibrium so the net torque must be zero. The two contributions to the torque come from the tension in the cord and the weight of the rod.

For the given setup the lever arms are , where L is the length of the rod. Therefore,

(b) The horizontal component of the hinge force is equal to, and opposes, the horizontal wire tension: 32 N. The vertical component of the hinge force is equal to, and opposes, the rod weight: (3.1 kg)(9.81 m/s²) = 30 N.

41. Since the force is tangential, the torque is t = rF = Ia, where and a can be written as a = Dw/Dt. Putting these together gives

59. The initial angular velocity is

By the conservation of angular momentum,

69. One complete turn = 2p rad

Selected Solutions by David Reid, Eastern Michigan University. ©2002 by Prentice Hall, Inc.

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