# Particle motion in Center of Momentum frame

I am studying about the center of momentum from Wikipedia. It is defined as the frame in which the total linear momentum of the system of particles vanishes and that the center of mass is but a special case of it. There it is given the following:

If $$S$$ is the laboratory frame and $$S'$$ be the center of momentum frame. Then, after a Galilean transformation, $$v'=v-V$$ where $$V$$ is the velocity of the center of mass which, I suppose, is measured in the laboratory frame. Also $$v$$ be the velocity of a particle in the lab frame. So the above equation must logically mean that $$v'$$ is the velocity of the particle in the center of mass frame. But Wikipedia says that $$v'$$ is the velocity of particle in the center of momentum frame. How can we justify this in a situation where center of mass is not the same as center of momentum?

• Does this answer your question? "In all center-of-momentum frames, the center of mass is at rest, but it is not necessarily at the origin of the coordinate system." In other words: in every center of momentum frame, the center of mass is at rest. But only in the center of mass frame is the center of mass also at the origin. Jan 11 at 15:16
• @AccidentalTaylorExpansion I think I get it now. It means that when they are same, both are attached at origin. When they are different, they are at 0 relative speed but at different positions. Jan 11 at 15:36