In-plane inertia isotropy of a square plate
= In-plane inertia isotropy of a square plate
{title2=$I_\phi=Ml^2/12$}
A uniform thin square of side $l$ and <mass> $M$ has $I_z=Ml^2/6$ about the perpendicular central axis. Any central in-plane axis and its perpendicular in-plane partner have equal moments by $90^\circ$ rotational symmetry. The <perpendicular axis theorem> says their sum is $I_z$, proving $I_\phi=Ml^2/12$ for every angle $\phi$. A non-square rectangle generally lacks this angle independence.