How Long Is the Track on a Full-Length CD When Stretched Straight?

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Homework Statement


Compact Disc. 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.

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?

Homework Equations


theta = (w_f + w_0)t
s = r*theta

w = angular velocity

The Attempt at a Solution


This is part 3 of the problem so I already have the angular velocity for the innermost and outermost of the disc--which I assume it is the initial and final angular velocity. Pls correct me if I'm wrong. I've used the eqns above to find theta and the length but I'm coming out with the wrong answer, 5.25km. I took the outer radius - inner radius = r. Can someone pls correct me? I don't know what I'm doing wrong. :frown:

Edit: Nvm. I was thinking way too complicated. ><;
 
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As the disc spins inside a CD player, the track is scanned at a constant linear speed of 1.25 m/s.

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?

If it is being tracked at constant linear speed as you said, then you can simply multiply the linear speed by the playing time in seconds to get your answer.:smile: