* The moment of inertia depends upon how an object's mass is distributed relative to it pivot point.

For a solid dm = r dV where r is the density function and dV is a differentially small volume.

* A body does not have just one moment of inertia but potentially an infinite number of I's, one for every different pivot point.

* For a fixed pivot point, an object has only one value for its moment of inertia independent of the torques acting on it. In other words, the torque acting on a body does not affect its moment of inertia.

Units:
SI: kg m²

Parallel-Axis Theorem:

There is a simple relationship between the moment of inertia about the center of mass of a body I_cm and the moment of inertia about some other point that is a distance d from the center of mass provided both axes of rotation are parallel.

* If you know the moment of inertia about the center of mass you, can find it about ANY pivot point by using the parallel axis theorem, provided the axis of rotation is parallel.

Moment of Inertia of Simple Solids: