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# moment of Inertia

Asked by harshveer262006 9th January 2023, 9:41 PM
Fig.(1) shows the moment of inertia of disk of radius R with respect to the rotation axis perpendicular to the
plane of disk and passing through centre of mass.

Let the axis of rotation in fig.(1) coincide with z-axis of cartesian coordinate system.

Then
where M is mass of disc .

If our axis of rotation is either x-axis or y-axis as shown in fig.(2) ,
by perpendicular axis theorem

By symmetry Ix = Iy

Hence Iy = (1/2) Iz = (1/2) (1/2) M R2 = (1/4) M R2

If axis of rotation is shifted to the edge of disc as shown in figure ,

Then by parallel axis theorem ,

Answered by Expert 10th January 2023, 12:03 AM
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