Category:Examples of Center of Mass
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This category contains examples of Center of Mass.
Let $B$ be a body of mass $M$.
Discrete
Let $B$ be made up of $n$ discrete particles each with:
- mass $m_i$
- position vector $\mathbf r_i$
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:
- $\ds M \bar {\mathbf r} = \sum_{i = \mathop 1}^n m_i \mathbf r_i$
Continuous
Let $B$ be of density $\map \rho {\mathbf r}$ at the point with position vector $\mathbf r$.
The center of mass of $B$ is the point whose position vector $\bar {\mathbf r}$ is given by:
- $\ds M \bar {\mathbf r} = \int_V \map \rho {\mathbf r} \mathbf r \rd V$
where:
- $V$ is the volume of space occupied by $B$
- $\d V$ is an infinitesimal volume element
- $\mathbf r$ is the position vector of $\d V$.
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