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prob_010 - 10 REASONING The centripetal acceleration for...

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10 . REASONING The centripetal acceleration for any point that is a distance r from the center of the disc is, according to Equation 5.2, a c = v 2 / r . From Equation 5.1, we know that v r T = 2 π / where T is the period of the motion. Combining these two equations, we obtain a r T r r T c = = ( / ) 2 4 2 2 2 π π SOLUTION Using the above expression for a c , the ratio of the centripetal accelerations of the two points in question is a a r T r T r T r T 2 1 2 2 2 2 2 1 1 2 2 2 2 1 1 2 4 4 = = π π / / / / Since the disc is rigid, all points on the disc must move with the same period, so T 1 = T 2 . Making this cancellation and solving for
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