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 24.0 mm and 57.5 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.38 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 77.5 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 77.5-min playing time? Take the direction of rotation of the disc to be positive.
rad/s2

Explanation / Answer

(A) v = 1.38 rad/s

w = v / r

w_innermost = 1.38 / (24 x 10^-3)

= 57.5 rad/s

w_outermost = 1.38 / (57.5 x 10^-3)

= 24 rad/s

(B) d = v t

d = (1.38 m/s) (77.5 x 60 sec)

d = 6417 m

(C) wf = 24 rad/s

wi = 57.5 rad/s

t = 77.5 x 60 sec

average angular acceleration = change in angular speed / time

= (57.5 - 24) / (77.5 x 60)

= 7.204 x 10^-3 rad/s^2

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