# Center of Mass

Written by Jerry Ratzlaff on . Posted in Relativity

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 Calculation for Two Masses

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