Momentum conservation

Momentum
Momentum of a pool cue ball is transferred to the racked balls after collision.
Common symbols	p, p
SI unit	kilogram meter per second kg · m/s
Other units	slug · ft/s
Conserved?	yes

In classical mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta; SI unit kg · m/s) is the product of the mass and velocity of an object, quantified in kilogram-meters per second. It is dimensionally equivalent to impulse, the product of force and time, quantified in newton-seconds. Newton's second law of motion states that the change in linear momentum of a body is equal to the net impulse acting on it. For example, a heavy truck moving rapidly has a large momentum, and it takes a large or prolonged force to get the truck up to this speed, and would take a similarly large or prolonged force to bring it to a stop. If the truck were lighter, or moving more slowly, then it would have less momentum and therefore require less impulse to start or stop.

Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude:

where p is the three-dimensional vector stating the object's momentum in the three directions of three-dimensional space, v is the three-dimensional velocity vector giving the object's rate of movement in each direction, and m is the object's mass.

Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change.

In classical mechanics, conservation of linear momentum is implied by Newton's laws. It also holds in special relativity (with a modified formula) and, with appropriate definitions, a (generalized) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is ultimately an expression of one of the fundamental symmetries of space and time, that of translational symmetry.