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/s2. 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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