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 3.50 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 0.0249 m from the center of a CD. (c) What angular acceleration does this imply?

Explanation / Answer

a)

tangential speed, v1 = r1*w1 = 0.0568*3.50*2*pi==1.25 m/s

b) The final angular speed is:

w2 = w1*(r1/r2) = 3.5*(0.0568/0.0249)= 7.98 rev/s

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