Definition:Center of Mass/Discrete

Definition

Let $B$ be a body of mass $M$.

Let $B$ be made up of $n$ discrete particles each with:

mass $m_i$

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

The center of mass of $B$ is the point whose position vector $\bar {\mathbf r}$ is given by:

$\ds M \bar {\mathbf r} = \sum_{i = \mathop 1}^n m_i \mathbf r_i$

The center of mass of a body is also known as its mass center.

Also note that in UK English, center is spelt centre.

Some sources use the term barycenter, but that term has wider applications than applied mathematics, and is used a more general concept in affine geometry.