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

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

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

${\displaystyle I\ {\stackrel {\mathrm {def} }{=}}\ \sum _{i=1}^{N}{m_{i}r_{i}^{2}}\,\!}$

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

${\displaystyle Torque=Ia\,}$