Find the moment of inertia of a uniform square plate of mass $M$ , edge of length $^{'} l^{'}$ about its axis passing through $P$ and perpendicular to it.

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Solution

Axis-1 & Axis-2 are perpendicular to each other and are in same plane so they can contribute in perpendicular axis theorem so moment of Inertia about an axis perpendicular to both 1 & 2 and passing through their intersection will be,

$I = I_{1} + I_{2}$ = $\frac{2 m l^{2}}{3}$

M.O.I about axis-1 is $I_{1}$ = $m l^{2} / 3$

M.O.I about axis-1 is $I_{2}$ = $m l^{2} / 3$

$I = I_{1} + I_{2} = \frac{2 m l^{2}}{3}$

M.O.I about axis-1 is $I_{1} = \frac{m l^{2}}{3}$

M.O.I about axis-2 is $I_{2} = \frac{m l^{2}}{3}$

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