Important Notice 

Rotational Inertia will not be on any tests (for me or for the AP Physics B test).  It is presented here only for completeness please don't spend a great deal of time on this concept. 

Important Equations 

slender rod:axis through centeraxis through end
rectangular plane:axis through centeraxis along edge
spherethin-walled hollowsolid
thin-walled hollow

What is Rotational Inertia

Rotational Inertia: to understand rotational inertia, we had better explain 
inertia in general.Inertial is a "resistance to change of motion". The more inertia
an object has, the less it responds to being pushed.  For linear motion (moving
from here to there), The measure of an object's inertia is its mass.  The more
mass in an object, the less it responds to being pushed.  A light push sends
a ping-pong ball flying, while a light push on a bowling ball has almost no
noticeable effect.

Rotational inertia is a resistance to change of rotation.  The more
rotational inertia an object has, the less it responds to being spun.  The
outside parts of a spinning object have to move much faster than inside
parts near the axis.  How an object is built, and along what direction you
want to spin it, also affect the rotational inertia.

Rotational Inertia