Let l be the moment of inertia of an uniform square plate about an axis AB that passes through its center and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the center of the plate and makes an angle θ with AB. The moment of inertia of the plate about the axis CD is then equal to

Question

Let l be the moment of inertia of an uniform square plate about an axis AB that passes through its center and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the center of the plate and makes an angle θ with AB. The moment of inertia of the plate about the axis CD is then equal to

Infinity Learn · Accepted Answer

Let IZ is the moment of inertia of square plate about the axis which is passing through the centre and perpendicular to the plane.$$IZ=IAB+IA$$'B'$$=ICD+IC$$'D'[By the theorem of perpendicular axis]$$IZ=2IAB=2IA$$'B'$$=2ICD=2IC$$'D' [As AB,A′B′ and CD,C′D′ are  symmetric axis]  Hence $$ICD=IAB=I$$

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