Let\'s begin with the angular acceleration of a compact disk (CD). To play music

Question

Let's begin with the angular acceleration of a compact disk (CD). To play music the CD must rotate at high speed while a laser reads data encoded in a spiral pattern on the disk. The disc has radius R=6.0cm=0.060m; when data are being read, it spins at 7200 rev/min. What is the CD's angular velocity in radians per second? How much time is required for it to rotate through 90? If it starts from rest and reaches full speed in 4.0 s, what is its average angular acceleration?

a) An old-fashioned vinyl record is designed to turn at 33 rev/min. Find the average angular velocity. Express your answer in radians per second to two significant figures.

b)Find the angular acceleration of the record if it spins through four and a half rotations before coming to a stop when the record player is turned off. Express your answer in radians per second squared to two significant figures.

Explanation / Answer

CD's angular velocity     =   (7200 * 2 * 3.14)/60

                                           = 753.6 rad/sec

time is required for it to rotate through 90 = 3.14/(2*753.6)   = 2.083 * 10-3 sec

average angular acceleration = 753.6/4   = 188.4 rad/sec2

a)     average angular velocity. =   (33 * 2 * 3.14)/60   = 3.454 rad/sec

b)     angular acceleration of the record = - ( 3.454)2/(2 * 4.5 * 2 * 3.14)

                                                             = - 0.211 rad/sec2

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