First slide

General Planar motion

Question

A body is rolling without slipping on a horizontal plane. The rotational energy of the body is 40% of the total kinetic energy. Identify the body.

Moderate

A

Ring
B

Hollow cylinder
C

Solid cylinder
D

Hollow sphere

Solution

$\frac{\frac{1}{2} I ω^{2}}{\frac{1}{2} M v^{2}} = \frac{40}{60} = \frac{2}{3} or \frac{\frac{I v^{2}}{R^{2}}}{M v^{2}} = \frac{2}{3} or I = \frac{2}{3} M R^{2}$
Clearly, the body is a hollow sphere.

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