= Solution
Use two central perpendicular axes in the plate. The <perpendicular axis theorem> and the preceding <moments of inertia> give
$$
\boxed{I_{z,G}=\frac{Ma^2}{12}+\frac{Ma^2}{12}=\frac{Ma^2}{6}.}
$$
Alternatively, axes along adjacent edges have <moments of inertia> $Ma^2/3$ each. The normal axis through their shared corner therefore has $2Ma^2/3$. It lies a distance $a/\sqrt2$ from the parallel normal axis through the centre, so the <parallel axis theorem> yields $I_{z,G}=2Ma^2/3-M(a^2/2)=Ma^2/6$. This normal central result is independent of the in-plane axis-location ambiguity.
Back to article page
