<p align="right">Last Update: <font color="#4f81bd">November, 25, 2024</font></p>
## BIG IDEAS
- Moment of inertia is the rotational equivalent of mass.
### Definition
Moment of inertia is the measure of resistance to [[rotational motion]].
### Symbol
$I$
### SI Unit
SI unit is $kg \cdot m^2$
### Formulas
Rearrange the [[angular momentum]] definition to isolate $I$.
$I = \frac{L}{w} \tag{1}$
Where
$I$ is the moment of inertia,
$L$ is the [[angular momentum]], and
$\omega$ is the [[angular velocity]]
For a discrete system
$I = \Sigma m r^2 \tag{2}$
Where
$m$ is the mass of each point,
$r$ is the perpendicular distance from the axis of rotation to the point mass.
For a continuous system
$I = \int r^2 \ dm \tag{3}$
### Related Topics
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[[Home|Home]] | [[Rotational Motion]] | [[Torque]] | [[Moment of Inertia]] |[[Angular Momentum]]