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 , the moment of inertia about the axis is

where

  • is the mass
  • is the perpendicular distance from the mass to the axis of rotation

The SI unit for moment of inertia is . It has a dimension of

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.