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.

Explanation / Answer

a)
given

r1 = 0.0568 m

w1 = 3.5 rev/s

= 3.5*2*pi rad/s

= 21.99 rad/s

so, tangetial speed, v1 = r1*w1

= 0.0568*21.99

= 1.25 m/s <<<<<<<<------------Answer

b) in both cases tangetial speed should be same.

Apply, v2 = v1

r2*w2 = r1*w1

w2 = w1*(r1/r2)

= 3.5*(0.0568/0.0249)

= 7.98 rev/s <<<<<<<<------------Answer

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