A square plate of mass M and edge L is shown is figure. Find the moment of inertia of the plate about the axis in the plane of plate passing through one of its vertex making an angle $15^{\circ}$ from horizontal.

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Solution

$M o I$ of sq. plate $= \frac{1}{6} {M L}^{2}$
By parallel axis theorem
$M o I$ about one corner to its plane
$: - \frac{1}{6} {M L}^{2} + M ({\frac{5}{4} L}^{2})$
But axis makes $15^{\circ}$ with horizontal
$∴ M o I = \frac{(\frac{17}{12} M L^{2})}{sin 15^{\circ}} = \frac{17 \sqrt{2}}{6 (\sqrt{3} - 1)} {M L}^{2}$

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A square plate of mass M and edge L is shown is figure. Find the moment of inertia of the plate about the axis in the plane of plate passing through one of its vertex making an angle 15∘ from horizontal.

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