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.

Part A

If the CD rotates clockwise at 500rpm (revolutions per minute) while the last song is playing, and then spins down to zero angular speed in 2.60s with constant angular acceleration, what is ?, the magnitude of the angular acceleration of the CD, as it spins to a stop?

Part B

How many revolutions does the CD make as it spins to a stop?

Explanation / Answer

Angular velocity,

               = 500 rpm = 500 rv/60s

                  = 8.33 rps = 8.333x2 rad/s

                  = 52.35 rad/s

            
Angular acceleration,

         = (2 - 1)/t = (0 - 52.35 rad/s)/2.60 s

            = 20.13rad/s2

No of complete revolutions = Angular displacement,

      Average velocity =Displacement/time

     Displacement =avxtime=  0.5x(2+1)xt

                         = 0.5(0 +500 rpmx 2.6/60

                        = 500x1.3/60 = 10.83 rev

No of complete rev = 10

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