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You may recall from physics the relationship
\[ T = I \alpha \text{.} \nonumber \]
This formula is the rotational analog of Newton's second law \(F = ma\text{.}\) Here, the \(I\) represents the mass moment of inertia, which is the three-dimensional measure of a rigid body’s resistance to rotation around an axis. Mass moment of inertia plays the same role for angular motion as mass does for linear motion.
Mass moment of inertia is defined by an integral equation identical to (10.1.3), except that the differential area \(dA\) is replaced with a differential element of mass, \(dm\text{.}\) The integration is conducted over a three dimensional physical object instead of a two dimensional massless area.
The units of mass moment of inertia are \([\text{mass}][\text{length}]^2\text{,}\) in contrast to area moment of inertia's units of \([\text{length}]^4\text{.}\)
Mass moments of inertia are covered in more detail and used extensively in the study of rigid body kinetics in Engineering Dynamics.
