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The center of momentum frame is also called the center of mass frame (a less preferred term) CM frame, COM frame, or zero-momentum frame. It is defined as being the particular inertial frame in which the center of mass of a system of interest is at rest (has zero velocity).

The reason "center of mass frame" is not preferred, is that the center of mass is a point, and would not, by itself, define an inertial frame. Moreover, since the "center of momentum" of a system is not a point in space, but rather actually refers to the center of momentum frame, the term "center of momentum" is synonymous with, and a short term for, the COM frame.

[edit] Properties

In this special inertial frame where the center of mass it at rest, the total linear momentum of the system is zero. Also, the total energy of the system is the minimal energy as seen from all possible inertial reference frames. In the COM frame, the total energy of the system is the "rest energy", and this quantity (when divided by the factor c²) therefore gives the rest mass or invariant mass of the system.

[edit] Example problem

An example of the usage of this frame is given below - in a two-body elastic collision problem. The transformations applied are to take the velocity of the frame from the velocity of each particle:

where is given by:

If we take two particles, one of mass m₁ moving at velocity V₁ and a second of mass m₂, then we can apply the following formulae:

After their collision, they will have speeds: