Conservation of Momentum in a System of Particles

If we have a system with particles with masses , velocities , and momenta , the total momentum is:

or:

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The total momentum of a system of particles is equal to the product of the total mass of a system and the velocity of its center of mass.

using Center of Mass. So:

If we view the system from a frame of reference that is moving with the center of mass , then in this frame the velocity of a particle in the system is

In the reference frame of the center-of-mass, the total momentum is

In the center-of-mass reference frame, the total momentum is zero.