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

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; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s.

Part A

What is the angular speed of the CD when scanning the innermost part of the track?

Part B

What is the angular speed of the CD when scanning the outermost part of the track?

Part C

The maximum playing time of a CD is 74.0 min. What would be the length of the track on such a maximum-duration CD if it were stretched out in a straight line?

Part D

What is the average angular acceleration of a maximum-duration CD during its 74.0-min playing time? Take the direction of rotation of the disc to be positive.

Explanation / Answer

"A compact disc (CD) stores music in a coded pattern of tiny pits 10?7m deep. The pits are arranged in a track that spirals outward toward the rim of the disc; the inner and outer radii of this spiral are 25.0 mm and 58.0 mm, respectively. As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s."

? = v / r

A) ? = 1.25m/s / 0.025m = 50 rad/s

B) ? = 1.25m/s / 0.058m = 21.6 rad/s

C) d = v * t = 1.25m/s * 74min * 60s/min = 5550 m = 5.55 km

D) ? = ?? / ?t = (21.6 - 50)rad/s / (74min * 60s/min) = -0.0064 rad/s

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