Moment of Inertia of a Continuous Body

Vocabulary flashcards covering basic formulas and definitions for the moment of inertia of continuous bodies and a uniform rod from lecture notes.

Moment of Inertia of a Continuous Body

The general integral formula used to calculate the moment of inertia of a continuous mass distribution, expressed as $I = \int r^2\,dm$.

Mass Element ($dm$) of a Uniform Rod

The mass of a small segment $dx$ for a rod of uniform mass $m$ and total length $l$, defined as $dm = \frac{m}{l}\,dx$.

Moment of Inertia of a Uniform Rod (Central Axis)

The moment of inertia of a uniform rod of mass $m$ and length $l$ about an axis perpendicular to its length through its center, derived by integrating from $-l/2$ to $l/2$ to yield $I = \frac{m l^2}{12}$.