Question

A man stretching in free space changes the shape of his body, e.g by spreading his arms or curling up. By doing this, he can change his

• A. moment of inertia
• B. angular momentum
• C. angular velocity
• D. rotational kinetic energy

Answer 1

The correct option is D rotational kinetic energy

Since, there is no external torque on man.

$\tau =0=\frac{dl}{dt}$

$\Rightarrow L=constant$

By stretching, he distributes his mass away from his natural axis of rotation.

Hence, he can increase his moment of inertia by stretching & decrease it by curling.

$L=I\omega$

$L$ is constant $\Rightarrow \omega$ changes with $I$.

Rotational Kinetic Energy$=\frac{1}{2}I{\omega }^2=\frac{I^2{\omega }^2}{I}=\frac{L^2}{2I}$

$\Rightarrow RotationalKEchangeswithI$