A solid sphere (I = \tfrac{2}{5}M R^2) rolls without slipping at speed v. The fraction of its total KE that is <strongrotational</strong is

2/7 Trans: \tfrac{1}{2}M v^2. Rot: \tfrac{1}{2}\cdot\tfrac{2}{5}M R^2 (v/R)^2 = \tfrac{1}{5}M v^2. Total \tfrac{7}{10}M v^2. Rotational fraction: (1/5)/(7/10) = 2/7.

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Rotational Kinetic Energy

AP Physics 1· difficulty 3/5

I = \tfrac{2}{5}M R^2

A
$2/5$
B
$1/2$
C
$2/7$
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D
$1/5$

Explanation

\tfrac{1}{2}M v^2

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AP Physics 1 · Rotational Kinetic Energy Practice Question | Acemy