Center of Mass

The terms "center of mass" and "center of gravity" are used synonymously in a uniform gravity field to represent the unique point in an object or system which can be used to describe the system's response to external forces and torques. The concept of the center of mass is that of an average of the masses factored by their distances from a reference point. In one plane, that is like the balancing of a seesaw about a pivot point with respect to the torques produced.
If you are making measurements from the center of mass point for a two-mass system then the center of mass condition can be expressed aswhere r₁ and r₂ locate the masses. The center of mass lies on the line connecting the two masses.