Question

When no external torque acts on a rotating system,

• A. angular momentum of the system is not conserved
• B. its rotational kinetic energy is conserved
• C. its rotational kinetic energy is independent of moment of inertia
• D. its rotational kinetic energy is directly proportional to moment of inertia
• E. its rotational kinetic energy is inversely proportional to moment of inertia

Answer 1

Answer: (E)

According to the law of conservation of angular momentum, when no external torque acts on rotating object, angular momentum remains conserved.
However, rotational kinetic energy is given as
$(KE{)}_R=\frac{1}{2}I{\omega }^2$
where, $I$ is moment of inertia and $\omega$ is angular frequency.
$\Rightarrow (KE{)}_R\propto I$