Question

Two rigid bodies have same moment of inertia about their axes of symmetry. Of the two, which body will have greater kinetic energy?

Answer 1

we know, rotational kinetic energy is given by
$K.E_{\textbf{rotational}}=\frac{1}{2}I\omega^2$........(1)
where I denotes moment of inertia and $\omega$ denotes angular velocity.

we know, $L=I\omega$, where L denotes angular momentum.

or, $\omega=\frac{L}{I}$, put it in equation (1),

so, $K.E_{\textbf{rotational}}=\frac{1}{2}\frac{L^2}{I}$

here external torque, $\tau_{\textbf{external}}$ = 0,
so, angular momentum remains constant.

or, $K.E_{\textbf{rotational}}\propto\frac{1}{I}$

hence,The rigid body having less moment of inertia will have greater kinetic energy.