Moment of Inertia

Definition

Moment of inertia measures resistance to rotational motion.

$$ I = \sum m_i r_i^2 $$

For Continuous Bodies

$$ I = \int r^2 \, dm $$

Examples

• Point mass:

$$ I = mr^2 $$

• Ring:

$$ I = MR^2 $$

• Solid disk:

$$ I = \frac{1}{2}MR^2 $$