A solid sphere rolls without slipping on a horizontal surface. What fraction of its total kinetic energy is rotational?

2/5
2/7
1/5
7/10

Correct answer: 2/7

Solution

KE_rot = (1/2)*I*omega² = (1/2)*(2mR²/5)*(v/R)² = mv²/5. KE_trans = mv²/2. KE_total = 7mv²/10. Ratio = (mv²/5)/(7mv²/10) = 2/7.

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