Physics - Rotation Question with Solution | TestHub

Let the square plate lie in the $xy$-plane with one of its corners at the origin and its adjacent sides along the $x$ and $y$ axes.

The moment of inertia of the plate about the $x$-axis (which lies along one edge) is $I_x=\frac{m{a}^2}{3}$.

The moment of inertia of the plate about the $y$-axis (which lies along the adjacent edge) is $I_y=\frac{m{a}^2}{3}$.

By the perpendicular axis theorem, the moment of inertia about the $z$-axis (which is perpendicular to the plane and passes through the corner) is given by:

$I_z=I_x+I_y$

$I_z=\frac{m{a}^2}{3}+\frac{m{a}^2}{3}=\frac{2m{a}^2}{3}$

Answer: $\frac{2m{a}^2}{3}$