Define perpendicular axis theorem of moment of inertia.

Explanation

Statement: The moment of inertia of a plane lamina about an axis perpendicular to plane lamina is the sum of moments of inertia about any two mutually perpendicular axes both lying in plane lamina.
Let `I_x and I_y` be moment of inertia about X and Y axis, then `I_Z` (moment of inertia about Z-axis) is
`I_Z =I_X +I_Y`

Proof
Consider a particle of mass m of plane lamina lying at point P at a distance r from O.
Let (x, y) be the coordinates of point P. The moment of inertia of particle at P about Z-axis = `mr^2` .
Then moment of inertia of whole plane lamina about Z-axis is
`I_Z = summr^2 = summ (x^2+y^2)`
Here `r^2 =x^2+y^2`
`I_z= summx^2+summy^2`
So `I_Z= I_X+I_Y`
where `I_x = summx^2` = = moment of inertia of plane lamina about X-axis.
`I_y= summy^2` = moment of inertia of plane lamina about Y-axis.
Thus . `I_Z= I_x+I_y` is the required proof of theorem of perpendicular axis of moment of inertia.