A computer is reading data from a rotating CD-ROM. At a point that is 0.031 m from the center of the disc, the centripetal acceleration is 126 m/s^{2}. What is the centripetal acceleration at a point that is 0.058 m from the center of the disc?

If w is the angular speed of the disk, the centripetal acceleration at a distance r from the center is:

a = rw^2.

w^2 = a / r

As w is constant for the whole disc:

a1 / r1 = a2 / r2

a2 = r2 a1 / r1.

Putting r1 = 0.031 m, a1 = 126 m/s^2, r2 = 0.058 m:

a2 = 0.058 * 126 / 0.031

= 236 m/s^2.

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