Momentum is a fundamental quantity in mechanics that is conserved in the absence of external forces. Conservation of momentum follows from invariance under translation by Noether's symmetry theorem. A similar quantity conserved in the absence of noncentral forces is called angular momentum.

For a single particle of mass m with velocity v, the momentum is defined as

(1)

From Newton's second law, a force F produces a change in momentum

(2)

Therefore, if , then

(3)

and

(4)

so the particle has constant velocity.

Angular Momentum, Conservation of Momentum, External Force, Force, Impulse, Inertia, Mass, Momentum Commutator, Momentum Density, Momentum Four-Vector, Newton's Second Law, Velocity