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

$I\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}m{r}^2$

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

$I\stackrel{\mathrm{d}\mathrm{e}\mathrm{f}}{=}\sum _{i=1}^N{m}_i{r}_i^2$

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

$Torque=Ia$