Question

write the Theorem of Perpendicular Axes​

Answer 1

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This theorem relates the moment of inertias of a laminar object about three mutually perpendicular and concurrent axes, two of them in the plane of the object and the third perpendicular to the object. Laminarobject is like a leaf, or any two dimensional object, e.g., a ring, a disc, any plane sheet, etc.

rigid laminar object able to rotate about three mutually perpendicular axes x, y and z. Axes x and y are in the plane of the object while the z axis is perpendicular to it, and all are concurrent at O. Consider a mass element dm located at any point P. PM = y and PN = x are the perpendiculars drown from P respectively on the x and y axes.

Answer 2

Explanation:

Perpendicular Axis Theorem

The perpendicular axis theorem for planar objects can be demonstrated by looking at the contribution to the three axis moments of inertia from an arbitrary mass element. From the point mass moment, the contributions to each of the axis moments of inertia are