Question

A body of mass $m$ and radius of gyration $K$ has an angular momentum $L.$Then its angular velocity is

• A. $Lm{K}^2$
• B. $m{K}^2/L$
• C. $L/m{R}^2$
• D. none of thees

Answer 1

The correct option is C $L/m{R}^2$

We know that,

Inertia of any body is equal to mass times square of radius of gyration.

i.e.,

$I=m{R}^2$

where, $R\to$ radius of gyration

And, angular momentum$\left(L\right)$:

$L=I\omega$ where, $\omega \to$ angular velocity

$L=m{R}^2\omega$

so, $\omega =\frac{L}{m{R}^2}$.