Question

What is the difference beween polar moment of inertia,mass moment of inertia and area moment of inertia?

Answer 1

1) POLAR MOMENT OF INERTIA: is the inertia in rotating an object around a point.

An object rotated around a point with little polar moment of inertia will rotate easily. If it has a higher moment of inertia, it will need more torque to rotate it.

Newton's second law for torques:
T = Ia

2) MOMENT OF INERTIA: of a body is the summation of th masses of the point masses multiplied by the square of their distances (displacement vectors) from the origin (mainly centre of mass or the axis of rotation)
It is given as :-

I = Σmkrk².

3) For AREA MOMENT OF INERTIA.
 It takes little more time to derive for an ellipse.
You go through this site:
http://emweb.unl.edu/negahban/em223/note...

Answer 2

$<bodybgcolour=aqua><marquee><fontcolour=red>$ Moment of inertia of a body about a given axis is the sum of the products of masses of all the particles of the body and squares of their respective perpendicular distance from the axis of rotation.