# Center of Mass

## Center of Mass

Center of mass or center of gravity is a specific point in a system in reference to a mass. The center of mass of a rigid object is a fixed point in relationship to the mass.

### Center of Mass formula

A system at a specific time, on the same axis, having two masses.

\(\large{ x_{cm} = \frac {m_1 x_1 \;+\; m_2 x_2 } {m_1 \;+\; m_2} }\)

Where:

\(\large{ x_{cm} }\) = center of mass

\(\large{ m_1 }\) = mass 1

\(\large{ m_2 }\) = mass 2

\(\large{ x_1 }\) = position 1

\(\large{ x_2 }\) = position 2

### Center of Mass Multiple Masses formula

A system at a specific time, on the same axis, having multiple masses.

\(\large{ x_{cm} = \frac {m_1 x_1 \;+\; m_2 x_2 \;+\; \;\cdots } { m_1 \;+\; m_2 \;+\; \;\cdots } }\)

Where:

\(\large{ x_{cm} }\) = center of mass

\(\large{ m_1 }\) = mass 1

\(\large{ m_2 }\) = mass 2

\(\large{ x_1 }\) = position 1

\(\large{ x_2 }\) = position 2

Tags: Equations for Mass