A rigid body is in pure rotation.

The moment of inertia of a thin uniform square plate $ABCD$ of uniform thickness about an axis passing through the centre $O$ and perpendicular to the plate is

where $I_1$, $I_2$, $I_3$ and $I_4$ are, respectively, the moments of inertia about axes $1$, $2$, $3$ and $4$ which are in the plane of the plate.

In the figure shown a uniform rod of mass $m$ and length $l$ is hinged. The rod is released when the rod makes an angle $\mathrm{\theta }=60°$ with the vertical.

Consider a disc rolling without slipping on a horizontal surface at a linear speed $V$ as shown in the figure

A cylinder rolls without slipping over a horizontal plane with constant velocity. The radius of the cylinder is equal to $r$. At this moment