Center of Mass

Summary

The center of mass is a point where all the mass can be imagined to be located.

Key Equations:

COM for Descrite Masses:
${\vec{R}}_{c m} = \frac{1}{M} \sum_{i} m_{i} r_{i}$

COM for Continuous Masses
${\vec{R}}_{c m} = \frac{1}{M} \int r d m$

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Definition

The center of mass (COM) is a point where the average location of all the mass is. A point where you can imagine "all" the mass being located at. The location of the COM is a vector relative to a reference point, which can be arbitrarily chosen. Mathematically, it is defined below, where $m_{i}$ and $r$ is the displacement from the reference point and $M$ is the total mass.

\begin{matrix} Descrite Masses \\ {\vec{R}}_{c m} = \frac{1}{M} \sum_{i} m_{i} r_{i} \\ Continous masses \\ {\vec{R}}_{c m} = \frac{1}{M} \int r d m \end{matrix}

Common Misconception

Moment of Inertia describes how mass is disturbed relative to an axis.
Center of Mass describes a point where you can imagine all the mass to be located at relative to a reference point.

Definition

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