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

$I\ {\stackrel {\mathrm {def} }{=}}\ mr^{2}\,\!$

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.

$Torque=Ia\,$