First slide

Rolling motion

Question

A solid disc is rolling without slipping on a horizontal surface. Then what fraction of its total energy is produced due to the transnational motion of the disc ?

Easy

A

$\frac{3}{4}$
B

$\frac{2}{3}$
C

$\frac{1}{3}$
D

$\frac{4}{5}$

Solution

(2)
Energy due to transnational motion, $K_{T} = \frac{1}{2} m V^{2}$
Energy due to rotational motion,
$\begin{array}{l} K_{T} = \frac{1}{2} I_{C} . ω^{2} = \frac{1}{2} (\frac{1}{2} m R^{2}) {(\frac{V}{R})}^{2} = \frac{1}{4} m V^{2} \\ ∴ \frac{K_{T}}{K} = \frac{K_{T}}{K_{r} + K_{T}} = \frac{\frac{1}{2} m V^{2}}{\frac{1}{4} m V^{2} + \frac{1}{2} m V^{2}} = \frac{2}{3} \end{array}$

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