The moment of inertia of a square plate of si | vedclass

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(D) Let the square plate lie in the $xy$-plane with two of its sides along the $x$ and $y$ axes,meeting at the origin (the corner through which the ax

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$\frac{2}{3} M l^{2}$

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(D) Let the square plate lie in the $xy$-plane with two of its sides along the $x$ and $y$ axes,meeting at the origin (the corner through which the axis passes).According to the theorem of perpendicular axes,the moment of inertia about the $z$-axis (perpendicular to the plane) is $I_z = I_x + I_y$.The moment of inertia of a square plate of mass $M$ and side $l$ about an axis passing through one of its sides is $I = \frac{M l^2}{3}$.Here,$I_x = \frac{M l^2}{3}$ and $I_y = \frac{M l^2}{3}$.Therefore,$I_z = \frac{M l^2}{3} + \frac{M l^2}{3} = \frac{2}{3} M l^2$.

The moment of inertia of a square plate of side $l$ and mass $M$ about an axis passing through one of its corners and perpendicular to the plane of the square plate is given by:

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