First slide

Rolling motion

Question

A solid disc is rolling without slipping on a plane surface. If its kinetic energy of translation is 2 Joule, total kinetic energy of the disc

Moderate

A

6 Joule
B

4.5 Joule
C

3 Joule
D

4 Joule

Solution

Kinetic energy of translation, $K_{t} = \frac{1}{2} m ω^{2} R^{2}$
Total energy $E = \frac{1}{2} I ω^{2} + \frac{1}{2} m ω^{2} R^{2} = \frac{1}{2} (\frac{1}{2} m R^{2}) ω^{2} + \frac{1}{2} m ω^{2} R^{2}$
$= \frac{3}{4} {mω}^{2} R^{2} = \frac{3}{4} \times 2 K_{t} = \frac{3}{2} \times 2 Joule = 3 Joule$

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