A coin placed on a turntable rotating at 35.9 rev/min will stay there if its cen

Question

A coin placed on a turntable rotating at 35.9 rev/min will stay there if its center is placed no further than 7.3 cm from the axis of rotation. What is the maximum distance the center of the coin can be placed from the axis if the turntable rotates at 49.7 rev/min?

Explanation / Answer

Given that          1 = 35.9 rev/ min = 0.5983 rev / s          r1 = 7.3 cm =0.073 m          2 = 49.7 rev/ min = 0.82833 rev / s           r = ? We know that                        v = r ==>   1 / r Therefore we have                               r2 / r1 = 1 / 2                      ==> r2 = r1 * 1 / 2                                  = 0.073 * 0.5983 / 0.82833                                  = 0.0527 m                                  = 5.27 cm

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