A compact disc (CD) stores music in a coded pattern of tiny pits 10 -7 m deep. T

Question

A compact disc (CD) stores music in a coded pattern of tiny pits 10-7 m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; suppose the inner and outer radii of this spiral are 21.5 mm and 55.5 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.22 m/s. (a) What is the angular speed of the CD when the innermost part of the track is scanned? The outermost part of the track?

(b) If the maximum playing time of a CD is 71.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line?
km

(c) What is the average angular acceleration of a maximum-duration CD during its 71.0-min playing time? Take the direction of rotation of the disc to be positive.

Explanation / Answer

(A) v = 1.38 rad/s

innermost = v / r

= 1.22 / (21.5 x 10^-3)

= 56.7 rad/s

outermost = 1.22 / (55.5 x 10^-3)

= 21.98 rad/s

(B) d = v t

d = (1.22 m/s) (71 x 60 sec)

d = 5197.2 m

(C) f = 21.9 rad/s

i = 56.7 rad/s

t = 71 x 60 sec

average angular acceleration = change in angular speed / time

= (56.7 - 21.9) / (71 x 60)

= 8.169 x 10^-3 rad/s^2

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