# How does the radius affect the moment of inertia?

Mar 23, 2018

Moment of inertia is directly proportional to the square of the radius.

#### Explanation:

The moment of inertia, $I$, of a single mass, $M$, being twirled by a thread of length, $R$, is
$I = M \cdot {R}^{2}$

A body that is being rotated will closely resemble that relationship. The formulas for various geometric shapes are derived with integration. For example, for a solid sphere, moment of inertia is
$I = \left(\frac{2}{5}\right) \cdot M \cdot {R}^{2}$

I hope this helps,
Steve