What is the Moment of Inertia? A 10 Minute Introduction

[Greg Bernhardt]

Definition/Summary
The moment of Inertia is a property of rigid bodies.
It relates rotational force (torque) to rotational acceleration in the same way that mass relates ordinary (linear) force to ordinary acceleration.
Moment of Inertia has dimensions of distance squared times mass ($ML^2)$.
The moment of Inertia is always relative to a given axis. The same rigid body will usually have different Moments of Inertia for different axes.
Moment of Inertia is additive: the Moment of Inertia of a composite body is the sum of the Moments of Inertia of its parts (relative to the same axis).
Equations
Moment of inertia of rigid body about an axis, where r is the distance from that axis and $\rho$ is the density:
$$I\ \ =\ \int dm\ r^2\ =\ \int \rho dxdydz\ r^2$$
(for comprehensive lists of moments of inertia of specific bodies, see See Also)
Moment of momentum (angular momentum) about centre of mass, C:
$\ \ \ \ \boldsymbol{L}_C =...$

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