The moment of inertia measures an object’s resistance to a change in its rotational motion. It can be seen as analogous to mass, which measures an object’s resistance to a change in its translation motion.
Because it has to do with rotation, the moment of inertia is always measured about a reference axis, which is thought as the axis of rotation.
For a point mass
where
is the mass is the perpendicular distance from the mass to the axis of rotation
The SI unit for moment of inertia is
Moment of Inertia for Distributed Mass
If we have a distributed mass, we compute the moment of inertia by summing the contribution of each of its parts. If the mass has a continuous distribution, then this sum becomes an integral.