Center of Mass of System of Particles in Cartesian Plane

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Theorem

Let $B$ be a system of $n$ discrete particles embedded in a cartesian plane, each with:

mass $m_i$
position $\tuple {x_i, y_i}$

where $i \in \set {1, 2, \ldots, n}$.


Then the coordinates $\tuple {\bar x, \bar y}$ of the center of mass of $B$ are given by:

\(\ds M \bar x\) \(=\) \(\ds \sum_{i \mathop = 1}^n m_i x_i\)
\(\ds M \bar y\) \(=\) \(\ds \sum_{i \mathop = 1}^n m_i y_i\)

where:

$\ds M = \sum_{i \mathop = 1}^n m_i$


Proof


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Sources

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