# How is moment of inertia measured?

Moment of Inertia (MOI) is designated by the letter "I" and is measured by two variables: mass and radius, which are inverse to each other.

Here's the generic formula, which can take several forms: I = mr^2

In words, the equation can be summarized like this: Small objects with large mass rotate quickly. Large objects with small mass -- but greater cross-sectional area -- rotate slowly.

For example: Small dense objects, like ball bearings, have a small MOI; as a result, they rotate quickly and easily and find abundant use in gears, wheels and so on. Large empty objets, like hoops, have large MOI and consequently rotate slowly. Hard to get a hula hoop or a wagon wheel rotating fast.

The formula for MOI, as I mentioned earlier, has several variations, all of which depend on the shape of an object and its distribution of mass. You can look these up in any physics book or on Wikipedia. Here are a couple of examples:

point masses and hoops: I = mr^2
disks: I = 1/2(mr^2)
solid spheres: I = 2/5(mr^2)

Finally, MOI is directly proportional to torque. The larger the MOI, the more force needed to rotate an object.