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

Answer: (D)

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