The moment of inertia is given about an axis perpendicular to the plane of a circular disc. To find the moment of inertia about an axis along a diameter use the _____________.

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Solution

We have to use the perpendicular axis theorem because the moment of inertia of an axis perpendicular to the diameter is given.
Perpendicular axis theorem
For any body, the moment of inertia about axes perpendicular to the plane is equal to the sum of the moment of inertia of the plane about any two mutually perpendicular axes lying in the same plane.
$I_{z} = I_{x} + I_{Y}$ , where $I_{x}$ , $I_{Y}$ and $I_{Z}$ are moment of inertia about x, y, and z axes, respectively.
$∵$ To find the moment of inertia about an axis along a diameter, given the moment of inertia of a perpendicular axis, use the perpendicular axis theorem

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