Calculus II/Moments

The moment of inertia is sometimes called and referred to as "angular mass." It is the "amount of resistance" to changes in rotational motion.

The moment of inertia of a point mass m at a distance r from the axis of rotation is


 * $$I \ \stackrel{\mathrm{def}}{=}\ m r^2\,\!$$

The moment of inertia is additive, therefore, for a collection of $$N$$ point masses $$m_{i}$$ with distances $$r_{i}$$ to the rotation axis, the total moment of inertia is the sum of the point-mass moments of inertia


 * $$I \ \stackrel{\mathrm{def}}{=}\ \sum_{i=1}^{N} {m_{i} r_{i}^2}\,\!$$

The moment of inertia is commonly used to calculate torque when multiplied by the angular acceleration. This is analogous to F = ma.


 * $$Torque = Ia\,$$