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. SincevT=rωa 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. (b) the angular speed (in rev/s) for music at a distance of 0.0249 m from the center of a CD.

(a)

(b)

Explanation:

The tangential speed is related to the angular speed by the formula:

Where v is the tangential speed at a point a distance R from the axis of rotation, and ω is the angular speed (in rad/s). So, we can calculate the tangential speed at which music is detected, using the values for the outer edge of the CD. But first we have to express the angular speed in rad/s:

Now, we can plug in the given values in the formula above:

This means the music is detected at a tangential speed of 1.24m/s (a).

Next, we solve for ω and use this value for v to obtain the angular speed near the inner part of the disc:

Finally, we have to express this quantity in rev/s:

In words, the angular speed for music ar a distance of 0.0249m from the center of a CD is of 7.98rev/s (b).

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