A soccer ball of diameter and mass rolls up a hill without slipping, reaching a maximum height of above the base of the hill. We can model this ball as a thin-walled hollow sphere. What was its translational speed at the base of the hill? Assume no energy loss by friction. Leave your answer to 2 dp.
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We know that the moment of inertia of the soccer ball is I = 3 2 m r 2 .
Hence, by the conservation of energy, we have m g h = 2 1 m v 2 + 2 1 I ω 2 = 2 1 m v 2 + 2 1 × 3 2 m r 2 × r 2 v 2 = 6 5 m v 2 Hence, v = 6 g = 7 . 6 7 .