Physics - Rotation Question with Solution | TestHub

By the principle of conservation of angular momentum, the angular momentum $L$ of the system remains constant because no external torque acts on it.

The kinetic energy of a rotating body is given by $K=\frac{L^2}{2I}$, where $I$ is the moment of inertia.

Given that the initial kinetic energy is $K$ and the initial moment of inertia is $I$.

When the child stretches his arms, the new moment of inertia becomes $I^{\prime }=2I$.

The new kinetic energy $K^{\prime }$ is given by $K^{\prime }=\frac{L^2}{2I^{\prime }}=\frac{L^2}{2(2I)}=\frac{1}{2}\left(\frac{L^2}{2I}\right)=\frac{K}{2}$.

Answer: $\frac{K}{2}$