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

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 60.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.13 m/s. 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 If the maximum playing time of a CD is 75.0 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 What is the average angular acceleration of a maximum-duration CD during its 75.0-min playing time? Take the direction of rotation of the disc to be positive. rad/s^2

Explanation / Answer

Use equation,

= v / r

a) 1 = 1.13m/s / 0.024m = 47.08 rad/s

2 = 1.13m/s / 0.060m = 18.83 rad/s

b) d = v * t = 1.13m/s * 75min * 60s/min = 5085 m = 5.06 km

d) = /t = (18.83-47.08)rad/s/ (74min * 60s/min) = -0.0054 rad/s²

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