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

3/5
B

2/7
C

2/5
D

3/7

Solution

$\begin{array}{l} {KE}_{T otal} = \frac{1}{2} {IW}^{2} + \frac{1}{2} {MV}^{2} \\ = \frac{1}{2} \times \frac{2}{5} {MR}^{2} W^{2} + \frac{1}{2} {MV}^{2} \\ = \frac{1}{5} {MR}^{2} W^{2} + \frac{1}{2} {MV}^{2} = \frac{1}{5} {MV}^{2} + \frac{1}{2} {MV}^{2} \\ = \frac{7}{10} {MV}^{2} \end{array}$
$\begin{array}{l} {KE}_{rot} = \frac{1}{2} {IW}^{2} = \frac{1}{5} {MV}^{2} \\ \frac{{KE}_{rot}}{{KE}_{Total}} = \frac{\frac{1}{5} {MV}^{2}}{\frac{7}{10} {MV}^{2}} \\ = \frac{2}{7} \end{array}$

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