Section 10.8 Mass Moment of Inertia
You may recall from physics the relationship
\begin{equation*}
T = I \alpha\text{.}
\end{equation*}
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 angular acceleration around an axis. Mass moment of inertia plays the same role for rotational acceleration as mass does for linear acceleration.
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 \([\mathrm{mass}][\mathrm{length}]^2\text{,}\) in contrast to area moment of inertia’s units of \([\mathrm{length}]^4\text{.}\)
Mass moments of inertia are covered in more detail and used extensively in the study of rigid body kinetics in Engineering Dynamics.
