As you finish listening to your favorite compact disc (CD), the CD in the player

Question

As you finish listening to your favorite compact disc (CD), the CD in the player slows down to a stop. Assume that the CD spins down with a constant angular acceleration. If the CD rotates clockwise (let's take clockwise rotation as positive) at 500 rpm (revolutions per minute) while the last song is playing, and then spins down to zero angular speed in 2.60 seconds with constant angular acceleration, what is the angular acceleration of the CD, as it spins to a stop? Express your answer in radians per second squared.

Explanation / Answer

Angular velocity, w = 500 rpm = 500 rv/60s = 8.33 rps = 8.333x2pi rad/s = 52.35 rad/s
Angular acceleration, alpha= (w2 - w1)/t = (0 - 52.35 rad/s)/2.60 s = 20.13 rad/s^2
------------------------------------------------ Displacement = wavx time=0.5x(w2+w1)xt = 500x1.3/60
= 10.83 rev

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