A compact disc (CD) contains music on a spiral track. Music is put onto a CD wit

Question

A compact disc (CD) contains music on a spiral track. Music is put onto a CD with the assumption that, during playback, the music will be detected at a constant tangential speed at any point. Since vT = r, a CD rotates at a smaller angular speed for music near the outer edge and a larger angular speed for music near the inner part of the disc. For music at the outer edge (r = 0.0568 m), the angular speed is 4.07 rev/s. Find (a) the constant tangential speed at which music is detected and (b) the angular speed (in rev/s) for music at a distance of 0.0211 m from the center of a CD.

Explanation / Answer

Part A)

First 4.07 rev/s (times 2pi rad/rev) = 25.6 rad/s

Then v = wr

v = (25.6)(.0568)

v = 1.45 m/s

Part B)

For the different radius...

1.45 = .0211(w)

w = 68.8 rad/s (divide by 2pi and get)

10.96 rev/s (or 11.0 rev/s with rounding)

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