How hard it is to get something to spin, or to change an object's rate of spin, depends on the mass, the shape of the object, how the mass is distributed, and on the position of the axis of rotation. Rotational inertia, known as moment of inertia, accounts for all these factors.
The moment of inertia, I, is the rotational equivalent of mass.
For a simple object like a ball on a string, where all the mass is the same distance away from the axis of rotation:
I = mr2
If the mass is distributed at different distances from the rotation axis, the moment of inertia is determined by integrating:
| I | = | ò | r2 dm | = | S | m r2 |
We could work out this integral each time we wanted to know the moment of inertia of an object of a particular shape rotating about a particular axis, but it's much easier to look up expressions for I from the table on page 291 in the book.