Chapter 10: Rotational Kinematics and Energy Selected Solutions

Selected Solutions

15. Since the fan slows uniformly to a stop, we can take w_f = 0. It will be useful for both parts (a) and (b) to first determine the angular acceleration a:

(a) An expression that gives the angular displacement (or number of revolutions) is

(b) Using the same expression for the angular displacement except with w_f = 0.25 rev/s we get

25. (a) The relationship between linear (or tangential) and angular speed is w = v_t/r. This gives

(b) The centripetal acceleration is

41. (a) The angular acceleration is given by a = a_t/r. To get a_t we use

Therefore, we have

(b) Since a smaller r would result in an angular acceleration greater than that in part (a).

57. (a) We can use the conservation of mechanical energy of the system: U_i + K_i = U_f + K_f. This includes the rotational kinetic energy of the pulley. Initially, there is no kinetic energy K_i = 0 and we can take the reference of potential energy such that the final potential energy is zero U_f = 0. Therefore,

(b) The speed will decrease, because I_p is increased so more of the kinetic is used up in I_p rather than in v.

59. (a) Use the conservation of energy

(b) To determine the rotational kinetic energy, we need to know its speed which we can now determine from the above result for K_f.

(c) The translational kinetic energy is

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

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