First slide

General Planar motion

Question

If a spherical ball rolls on a table without slipping, the fraction of its total energy associated with rotation is

Moderate

A

$\frac{3}{5}$
B

$\frac{2}{7}$
C

$\frac{2}{5}$
D

$\frac{3}{7}$

Solution

$\begin{array}{l} f_{r} = \frac{\frac{1}{2} I ω^{2}}{\frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}}, where I = \frac{2}{5} m r^{2}, \\ ω = \frac{v}{r} \\ Solve to get f_{r} = \frac{2}{7} \end{array}$

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