Question

state and prove the theorem of perpendicular axes and parallel axes​

Answer 1

Answer:

The MOI around any axis is equal to the sum of moments of inertia about an axis parallel to the axis passing through the center of mass (COM) of the object and the product of the mass of the object with the square of the perpendicular distance from the axis in consideration and the COM axis parallel to it.

Answer 2

The perpendicular axis theorem states that the moment of inertia of a planar lamina (i.e. 2-D body) about an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia of the lamina about the two axes at right angles to each other, in its own plane intersecting each other at the point