# Q & A: Moment of inertia

Q:
Ok, I am doing a problem in 1999-2000 physics olympiad program. it said " the initial moment of inertia is 2000kg*m^2 " I want to know if inertia has a unit and how to define a inertia! Thanks A LOT!
- Isaac (age 15)
Toronto, Ontario,CA
A:
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)