Question

A body rotating about a fixed axis has a kinetic energy of $360J$ when its angular speed $30rad/sec$. The moment of inertia of wheel about its axis of rotation is

• A. $0.6kg-m^2$
• B. $0.15kg-m^2$
• C. $0.8kg-m^2$
• D. $0.75kg-m^2$

Answer 1

The correct option is (C) $0.8kg-m^2$

Kinetic Energy(KE)$=360J$

Angular Speed$=\omega =80rad/sec$

We know,

Kinetic energy is given as

$KE=\frac{1}{2}I{\omega }^2$

Or,

Putting values and solving

$I=\frac{2KE}{{\omega }^2}=\frac{2\times 360}{30\times 30}=0.8kg/m^2$

Hence the moment of inertia is $0.8$ kg/$m^2$