Question

A solid cylinder of mass M and radius R rotates about its axis with angular speed to. Its rotational kinetic energy is

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

Answer 1

Answer: (C)

$\frac{1}{4}MR^{2}\omega^{2}$

Answer 2

Moment of inertia of a the solid cylinder about its axis is

$I = \frac{MR^{2}}{2}$

$\therefore$Rotational kinetic energy of the cylinder is

$K = \frac{1}{2}I\omega^{2} = \frac{1}{2}\frac{MR^{2}}{2}\omega^{2} = \frac{1}{4}MR^{2}\omega^{2}$