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

Question

7.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.
(a) Find the constant tangential speed at which music is detected.
m/s

(b) Find the angular speed (in rev/s) for music at a distance of 0.0359 m from the center of a CD.
rev/s

Explanation / Answer

Tangential speed Vt = rw = 0.0568* 3.5*2*pi =1.249m/s (since 1rev/s = 2*pi rad/s) Vt=rw => w=Vt/r = 1.249/0.0249 = 50.16 rad/s = 7.9833 rev/s

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