Question

A quarter disc of radius $R$ and mass $m$ is rotating about the axis $O{O}^{\prime }$ (perpendicular to the plane of the disc) as shown. Rotational kinetic energy of the quarter disc is:

• A. $\frac{1}{2}m{R}^2{\omega }^2$
• B. $\frac{1}{4}m{R}^2{\omega }^2$
• C. $\frac{1}{8}m{R}^2{\omega }^2$
• D. $\frac{1}{16}m{R}^2{\omega }^2$

Answer 1

The correct option is D $\frac{1}{16}m{R}^2{\omega }^2$

Consider the axis of the rotation to the center of the origin full disc

Then,

Moment of inertia of full disc is $\frac{1}{2}m{r}^2$

Moment of inertia of quarter disc is one fourth of its original.

if the angular speed is $\omega$, then its rotational kinetic energy is

$\frac{1}{2}I{\omega }^2=\frac{1}{16}m{r}^2{\omega }^2$

Hence, Option $D$ is the correct answer.