Center of Mass for Particles

The center of mass is the point at which all the mass can be considered to be "concentrated" for the purpose for the purpose of calculating the "first moment", i.e., mass times distance. For two masses this distance is calculated from
For the more general collection of N particles this becomes
and when extended to three dimensions:
This approach applies to diccrete masses even if they are not point masses if the position x_i is taken to be the position of the center of mass of the i^th mass. It also points the way toward the calculation of the center of mass of an extended object.