# momentum

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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 |

Dimension | MLT^{−1} |

In Newtonian mechanics, **linear momentum**, **translational momentum**, or simply **momentum** (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If *m* is an object's mass and **v** is its velocity (also a vector quantity), then the object's momentum is:

In SI units, momentum is measured in kilogram meters per second (kg⋅m/s).

Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a *conserved* quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is an expression of one of the fundamental symmetries of space and time: translational symmetry.

Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems the conserved quantity is **generalized momentum**, and in general this is different from the **kinetic** momentum defined above. The concept of generalized momentum is carried over into quantum mechanics, where it becomes an operator on a wave function. The momentum and position operators are related by the Heisenberg uncertainty principle.

In continuous systems such as electromagnetic fields, fluid dynamics and deformable bodies, a momentum density can be defined, and a continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids.