Question

what is the moment of inertia?

Answer 1

a quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.

Answer 2

The moment of inertia of a rigid body about a fixed axis is defined as the sum of the products of masses of the particles constituting the body and the squares of their respective distances from the axis of rotation..
Let us consider a rigid body rotating with uniform angular velocity omega about an axis YY'.Suppose the body consists of n no. of particles of masses m1,m2,m3,..........mn situated at distances r1,r2,r3,.......rn  respectivly from the axis of rotation. The moment of inertia of the body about the axis YY' is given by
                    I=m1r1^2+m2r2^2+m3r3^2+.....................................+mn+rn^2