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 for two masses formula
\(\large{ x_{cm} = \frac {m_1\; x_1 \;+\; m_2 \; x_2 } {m_1 \;+\; m_2} }\)
Symbol	English	Metric
\(\large{ x_{cm} }\) = center of mass	\(\large{ ft }\)	\(\large{m}\)
\(\large{ m_1 }\) = mass 1	\(\large{ lbm }\)	\(\large{ kg }\)
\(\large{ m_2 }\) = mass 2	\(\large{ lbm }\)	\(\large{ kg }\)
\(\large{ x_1 }\) = position 1	\(\large{ ft }\)	\(\large{m}\)
\(\large{ x_2 }\) = position 2	\(\large{ ft }\)	\(\large{m}\)

 

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

Center of Mass Multiple Masses formula
\(\large{ x_{cm} = \frac {m_1 \; x_1 \;+\; m_2 \; x_2 \;+\; \cdots } { m_1 \;+\; m_2 \;+\; \cdots } }\)
Symbol	English	Metric
\(\large{ x_{cm} }\) = center of mass	\(\large{ ft }\)	\(\large{m}\)
\(\large{ m_1 }\) = mass 1	\(\large{ lbm }\)	\(\large{ kg }\)
\(\large{ m_2 }\) = mass 2	\(\large{ lbm }\)	\(\large{ kg }\)
\(\large{ x_1 }\) = position 1	\(\large{ ft }\)	\(\large{m}\)
\(\large{ x_2 }\) = position 2	\(\large{ ft }\)	\(\large{m}\)

 

Center of Mass for Two Masses calculator

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