Hi Isaac,
Yes, the moment of inertia does have a unit; it is kg*m^2, or
kilogram meters squared. This unit probably doesn't mean a lot to you
though, and you might be wondering what in the world a kilgram meter
squared is. Inertia is basically how hard it is to move something. If
an object has more inertia, it is harder to get it to move or to get it
to stop. For example, a truck has more inertia than a person does.
The moment of inertia is how hard it is to spin an object around a
certain axis. (For one object there are many different moments of
inertia because there are many different axes that the object can be
rotated around.) For example, take a meter stick and two weights, and
place the two weights at the center of the meter stick. Twirl the meter
stick like a baton and feel how hard it is to spin it. Now take the
same weights and instead of putting them in the center, put them at the
ends of the meter stick. Spin the meter stick again and compare how
hard it is to spin it.
In both cases, the mass was the same (meter stick plus two
weights), so how can it be that the meter stick is harder to spin when
the weights are on the ends instead of in the middle? The answer is
that the moment of inertia is larger when the weights are on the ends.
Remember that inertia has the weird unit of kilogram meters squared?
This comes from the product of a mass and a distance squared. This
makes sense -- if an object has more mass, then it is harder to move
and it has a larger moment of inertia. Also, as you discovered with the
meter stick, if the mass is farther away from where you are spinning
the object, it is harder to move the object and it has a larger moment
of inertia.
In summary, how hard it is to spin an object around a certain axis
not only depends on the mass of the object, but also where the mass is
located with respect to the axis. The difficulty of spinning an object
around an axis is called the moment of inertia.
(published on 10/22/2007)
