The moment of inertia (a.k.a. rotational
inertia) of a point mass, with respect to rotation about an axis
that is a distance *r* from the point mass, is the mass *m*
of the point mass times the square of the distance of the point
mass from the axis of rotation.

**Note 1:** It may be difficult to conceive of a
point mass in rotation about an axis of rotation some distance
from the point mass. It would seem that the point mass is going
around in a circle rather than spinning. It helps to imagine a
massless rod extending from the axis of rotation to the point
mass with the point mass fixed to the end of the rod. Then one
can think of the moment of inertia as the moment of inertia of
the massless rod with the point mass fixed to the end of the rod.
Such an object would be in rotational motion, spinning around on
the axis of rotation like the second hand spins around on a
clock. The moment of inertia of such an object with respect to
its axis of rotation would be I = mr^{2} and the moment
of inertia of such an object is what we mean by the moment of
inertia of the point mass (because the massless rod makes no
contribution to the moment of inertia).

**Note 2:** For the moment of inertia to be
exactly mr^{2}, the point mass really has to be a point
mass, having mass, but no extent in space. For an object, such as
a small metal ball, whose diameter is small compared to the
distance from the axis of rotation to the center of the object, I
= mr^{2} is a good approximation. (It is important to
realize that the r in such a case would be the large distance
from the axis of rotation to the center of the ball, not the
small radius of the ball.)