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Let l be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre 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
When a uniform square plate rotates about an axis in its plane, the moment of inertia depends on the orientation of the axis relative to the sides of the plate. Given that the moment of inertia about an axis parallel to two sides is denoted as l, and the axis CD makes an angle θ with this axis, theRead more
When a uniform square plate rotates about an axis in its plane, the moment of inertia depends on the orientation of the axis relative to the sides of the plate. Given that the moment of inertia about an axis parallel to two sides is denoted as l, and the axis CD makes an angle θ with this axis, the moment of inertia about axis CD is l/cos² θ.
This is because the rotational inertia depends on the distribution of mass relative to the axis of rotation. The cosine squared term accounts for the projection of the mass distribution onto the new axis.
Thus, the correct answer is that the moment of inertia about axis CD is l /cos² θ.
Checkout here : – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/
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