Steiner's Theorem

The moment of inertia \( I \) always refers to a specific axis of rotation. If the axis of rotation is changed, the moment of inertia of the rotating body also changes. It becomes larger, if you shift the rotation axis parallel by the distance \( h \) from the center of mass axis. The moment of inertia through the center of mass axis is \( I_\text{CM} \).

You can calculate the new moment of inertia with the following Steiner's theorem:

So, using Steiner's theorem, you can easily calculate the moment of inertia for a new axis of rotation without having to calculate a complicated integral.