**Theorem of perpendicular axis:** According to this theorem, "the moment of inertia of a planar body (lamina) about an axis OZ Perpendicular to the pane of the lamina (O being a point in this lamina) is the sum of the moments of inertia about any two mutually perpendicular axes OX and OY, both lying in the same plane",

Let I_{z} = moment of inertia of the lamina about OZ axis.

I_{x} = moment of inertial about Ox axis.

and l_{y} = moment of inertia about OY axis

Then, I_{z} = I_{x }+ I_{y}

**Proof **: Consider a particle of mass m of the lamina at point p distant r from O. Let (x, y) be point co-ordinates of the point P.(Fig).

The moment of inertia of the particle about z-axis = mr^{2}.

Moment of inertia of the whole lamina about z-axis is,