Conservation of momentum

In classical mechanics and quantum mechanics, momentum is a vector property of a particle. When no external force is acting on the particle, momentum is conserved (does not change in time, neither in magnitude nor direction).

The total momentum of a system of more than particle is defined as the vector sum of momenta of the individual particles. Because the particles in general exert a force on each other, in general the momenta of the individual particles in a many-particle system are not conserved. However, if the total external force on the system (force not exerted by the particles, but by some outside agent, such as for instance gravitation) is zero, then the total momentum of the many-particle system is conserved.