Solution: Rotational Energy

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This question seems quite complicated, but with conservation of energy, it is simplified.

E_i = E_f
(1/2)mv_1i² + f_kDx = (1/2)mv_2f² + (1/2)Iw

Use the fact that when the ball is not slipping, v = wR
(1/2)v_1i² + m_kgDx = (1/2)(wR)² + (1/2)(2/5)R²w²
(1/2)(10²) + 0.25g(8) = (7/10)w²(0.05²)
w = 200rev/sec

Answer: 200