Question

A rigid body of mass m rotates with angular velocity $\omega$ about an axis at a distance a from the centre of mass C. The radius of gyration about C is K. Then, kinetic energy of rotation of the body about new parallel axis is :

• A. $\frac{1}{2}m{K}^2{\omega }^2$
• B. $\frac{1}{2}m{a}^2{\omega }^2$
• C. $\frac{1}{2}m(a+K^2){\omega }^2$
• D. $\frac{1}{2}m(a^2+K^2){\omega }^2$

Answer 1

The correct option is D $\frac{1}{2}m(a^2+K^2){\omega }^2$

MI of body about centre of mass
$I_{cm}=m{K}^2$
MI of body about new parallel axis
$I_{new}=I_{cm}+m{a}^2=m{K}^2+m{a}^2=m(K^2+a^2)$
$\therefore$ Kinetic energy, $K=\frac{1}{2}{I}_{new}{\omega }^2$
$=\frac{1}{2}m(K^2+a^2){\omega }^2$