A rider on a mountain bike is traveling to the left. Each wheel has an angular v

Question

A rider on a mountain bike is traveling to the left. Each wheel has an angular velocity of +21.4 rad/s, where, as usual, the plus sign indicates that the wheel is rotating in the counterclockwise direction. (a) To pass another cyclist, the rider pumps harder, and the angular velocity of the wheels increases from 21.4 to 27.5 rad/s in a time of 3.40 s. (b) After passing the cyclist, the rider begins to coast, and the angular velocity of the wheels decreases from +27.5 to +15.6 rad/s in a time of 8.90 s. In both instances, (a) and (b), determine the direction and magnitude of the angular acceleration (assumed constant) of the wheels.

Explanation / Answer

a)

W = W0 + alpha*t

27.5 = 21.4 + alpha*3.4

=> alpha OR angular acceleration = 1.794 counterclockwise

b)

W = W0 + alpha*t

15.6 = 27.5 + alpha*8.9

=> alpha OR angular acceleration = -1.33 OR 1.33 in clockwise direction

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