In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object.

In physics, classical mechanics is one of the two major sub-fields of mechanics, along with quantum mechanics.

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It is a three-dimensional vector quantity, possessing a magnitude and a direction.

In mathematics, physics, and engineering, a Euclidean vector is a geometric object that has magnitude and direction.

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If m is an object's mass and v is the velocity, then the momentum is


{\displaystyle \mathbf {p} =m\mathbf {v},}


In SI units, it is measured in kilogram meters per second.

The kilogram is the base unit of mass in the metric system, formally the International System of Units, having the unit symbol kg.

S or s is the 19th letter in the Modern English alphabet and the ISO basic Latin alphabet.


Newton's second law of motion states that a body's rate of change in momentum is equal to the net force acting on it.

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics.


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.

A closed system is a physical system that does not allow transfer of matter in or out of the system, though, in different contexts, such as physics, chemistry or engineering, the transfer of energy is or is not allowed.

In physics, a frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements.


Momentum is also conserved in special relativity, and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity.

In theoretical physics, quantum field theory is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics but not general relativity's description of gravity.

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.

General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.


It is an expression of one of the fundamental symmetries of space and time: translational symmetry.

In geometry, to translate a geometric figure is to move it from one place to another without rotating it.

Symmetry in everyday language refers to a sense of harmonious and beautiful proportion and balance.


Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, allow one to choose coordinate systems that incorporate symmetries and constraints.

Hamiltonian mechanics is an equivalent but more abstract reformulation of classical mechanic theory.


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.

A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.

In physics, a wave is an oscillation accompanied by a transfer of energy that travels through a medium.


The momentum and position operators are related by the Heisenberg uncertainty principle.

In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which the values for certain pairs of physical quantities of a particle, such as position, x, and momentum, p, can be predicted from initial conditions.


In continuous systems such as electromagnetic fields, fluids 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.

In physics, the Navier–Stokes equations, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician George Gabriel Stokes, describe the motion of viscous fluid substances.

The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum.

A magnetic field is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials.

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