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

Question

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.

Part A

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

rad/s

Part B

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

rad/s

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.

rad/s

Explanation / Answer

A)There are 2pi(r) lengths of circumference around a circle of radius r and 2pi radians in each revolution
The inner track length is 2pi(0.025) m/rev = 0.05pi m
1.25 m/s / 0.05pi m/rev) = 25/pi rev/sec
at 2pi radians per revolution
25/pi(2pi) =50 rad/sec ANSWER

B) outer track same formulas
2pi(0.058) m/rev = 0.116pi m
1.25 m/s / 0.116pi m/rev) = 10.776/pi rev/sec
at 2pi radians per revolution
10.776/pi(2pi) =21.552 rad/sec ANSWER

C) 74 min (60 sec/min) (1.25 m/sec) = 5550 m ANSWER

D) as a cd normally starts at zero speed and acceleration and ends at the same condition. the average acceleration is (0-0)/74 or a = 0 rad/s/s ANSWER

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