Question

Define perpendicular axes theorem. Find the moment of inertia of a uniform circular ring about an axis passing through the diameter of the ring.

Answer 1

Answer:

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 where the perpendicular axis passes through it.

Define perpendicular axes displaystyle , displaystyle y}y, and {\displaystyle z}z (which meet at origin {\displaystyle O}O) so that the body lies in the {\displaystyle xy}xy plane, and the displaystyle z}z axis is perpendicular to the plane of the body. Let Ix, Iy and Iz be moments of inertia about axis x, y, z respectively. Then the perpendicular axis theorem states that[1]

Explanation: