Question

What is the moment of inertia used for?

Answer 1

Moment of inertia is the rotational analogue of mass.
Just like mass it determines the rotational kinetic energy.
It is to rotational mechanics, what mass is to translational motion.

For example, the rotational kinetic energy of a particle with moment of inertia `I` and angular velocity `omega` is given by,

`E""_(rot) = 1/2Iomega^2` , analogous to `E = 1/2mv^2`