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 23.5 mm and 54.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.34 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? Omega _innermost = rad/s omega_outermost = rad/s (b) If the maximum playing time of a CD is 79.5 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 79.5-min playing time? Take the direction of rotation of the disc to be positive. rad/s

Explanation / Answer

(a)

w= v/r

w_inner = 1.34/23.5 * 10^-3 = 57 rad/s

w_ outer = 1.34/54 * 10^-3 = 24.81 rad/s

(b)

d= vt = 1.34 ( 79.5 min) ( 60 s/ min) = 6.39 km

(c)

from the rotational kinematic equation

alpha = w_ 0-w_i/ t = 24.81-57/ 79.5 min) ( 60 s/ min= -6.74 * 10^-3 rad/s^2

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