The total 
of an object is the sum of the
of each piece and is separated into rotational and translational
. We will first consider
an object with no translational . The rotational
is then the total given by adding up 
for each
little piece of mass 
.
The quantity
is characteristic of the mass distribution and is a measure of the rotational inertia. It is called the moment of inertia,
The rotational
of an object is
Which is analagous to translational
.
The moment of inertia of an object depends on its mass, size, and shape.
increases as the mass is more concentrated toward the outside of the object. Thus objects of equal masses and even equal radii can have different moments of inertia. For a thin ring,
, and for a disk,
.
Integral calculus can be used to find the moment of inertia of many objects. The table below provides some results for objects of uniform density.
The mass of the object is
And the center of mass position is given by
The distribution of mass of an object is partly characterized by these so called moments:
,
, and
.
Fig 3 Moments of inertia for objects of several shapes calculated about a specific axis. In all cases, the mass of the object is