= Off-axis angular momentum of a square lamina
{title2=$|J|=\sqrt{10}\,ma^2\omega/24\quad(45^\circ)$}
For a uniform square of side $a$, the principal <inertia tensor> is $\operatorname{diag}(ma^2/12,ma^2/12,ma^2/6)$. A rotation axis tilted $45^\circ$ to the surface has equal in-plane and normal angular-velocity components. Multiplying each by its own principal moment gives the stated magnitude. In general $I_{\rm axis}\omega$ is only the axial projection of <angular momentum>.
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