State and explain parallel axis theorem and perpendicular axis theorem.

Explanation

Statement : The moment of inertia about an axis perpendicular to two other axes acting in the same plane with their point, is equal to intersection being a point on it and the (third) axis passing through the common point, is equal to the sum of moments of intertia about the two axes
e.g : `I_Z=I_X+I_Y`
Let M be the mass of the disk of radius R. M.I. about a point passing through the centre and perpendicular to the plane containing X and Y is `I_Z=(MR^2)/(2).`
Since X and Y are in the same plane, `I_X=I_Y`.
`therefore I_Z=I_x+I_Y` becomes `I_Z=2I_X`
hence `I_X=(I_Z)/(2)=(MR^2)/(4)`
i.e. moment of inertia of a circular disc about the diameter
`=(MR^2)/(4)`.