# Momentum

**conservation of momentumlinear momentummomentaconservation of linear momentummomentum conservationKinetic momentumrelativistic momentumlaw of conservation of momentumliftinglinear**

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.wikipedia

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### Quantum mechanics

**quantum physicsquantum mechanicalquantum theory**

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.

Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization), objects have characteristics of both particles and waves (wave-particle duality), and there are limits to the precision with which quantities can be measured (the uncertainty principle).

### General relativity

**general theory of relativitygeneral relativity theoryrelativity**

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.

In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present.

### Classical mechanics

**Newtonian mechanicsNewtonian physicsclassical**

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

Newton was the first to mathematically express the relationship between force and momentum.

### Wave function

**wavefunctionwave functionsnormalized**

The concept of generalized momentum is carried over into quantum mechanics, where it becomes an operator on a wave function.

In 1905, Einstein postulated the proportionality between the frequency f of a photon and its energy E, E = hf, and in 1916 the corresponding relation between photon's momentum p and wavelength \lambda, where h is the Planck constant.

### Hamiltonian mechanics

**HamiltonianHamilton's equationsHamiltonian dynamics**

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

In Cartesian coordinates, the generalized momenta are precisely the physical linear momenta.

### Collision

**collisionscollidecolliding**

This conservation law applies to all interactions, including collisions and separations caused by explosive forces.

### Center of mass

**center of gravitycentre of gravitycentre of mass**

A system of particles has a center of mass, a point determined by the weighted sum of their positions:

The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics.

### Translational symmetry

**translation invarianttranslational invariancetranslation invariance**

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

According to Noether's theorem, space translational symmetry of a physical system is equivalent to the momentum conservation law.

### Newton second

**newton-secondkg⋅m/sNewton seconds**

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

It is dimensionally equivalent to the momentum unit kilogram metre per second (kg·m/s).

### Impulse (physics)

**impulsetotal impulseimpulses**

, the change in momentum (or impulse

Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction.

### Rocket

**rocketsrocketryrocket scientist**

Rockets also make use of conservation of momentum: propellant is thrust outward, gaining momentum, and an equal and opposite momentum is imparted to the rocket.

To control their flight, rockets rely on momentum, airfoils, auxiliary reaction engines, gimballed thrust, momentum wheels, deflection of the exhaust stream, propellant flow, spin, or gravity.

### Euler's laws of motion

**Euler's equations of motionEuler's first lawEuler's laws**

:This is known as Euler's first law.

Euler's first law states that the linear momentum of a body,

### Newton's laws of motion

**Newton's second lawNewton's third lawNewton's second law of motion**

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.

In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities.

### Mass

**inertial massgravitational massweight**

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

Additionally, mass relates a body's momentum p to its linear velocity v:

### Velocity

**velocitiesvelocity vectorlinear velocity**

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

:ignoring special relativity, where E k is the kinetic energy and m is the mass. Kinetic energy is a scalar quantity as it depends on the square of the velocity, however a related quantity, momentum, is a vector and defined by

### Four-momentum

**4-momentumfour momentummomentum four-vector**

:and the (contravariant) four-momentum is

In special relativity, four-momentum is the generalization of the classical three-dimensional momentum to four-dimensional spacetime.

### Inelastic collision

**inelasticinelastic collisionsinelastic events**

If it is conserved, the collision is called an elastic collision; if not, it is an inelastic collision.

Although inelastic collisions do not conserve kinetic energy, they do obey conservation of momentum.

### Invariant mass

**rest massmassproper mass**

is the object's invariant mass.

More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations.

### Angular momentum

**conservation of angular momentumangular momentamomentum**

They introduce a generalized momentum, also known as the canonical or conjugate momentum, that extends the concepts of both linear momentum and angular momentum.

In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of linear momentum.

### Elastic collision

**elasticbouncescollision**

If it is conserved, the collision is called an elastic collision; if not, it is an inelastic collision.

The conservation of the total momentum before and after the collision is expressed by:

### Matter wave

**de Broglie wavelengthde Broglie relationde Broglie hypothesis**

, describes a de Broglie matter wave.

, associated with a massive particle and is related to its momentum,

### Euclidean vector

**vectorvectorsvector addition**

It is a vector quantity, possessing a magnitude and a direction.

Vectors also describe many other physical quantities, such as linear displacement, displacement, linear acceleration, angular acceleration, linear momentum, and angular momentum.

### Mass–energy equivalence

**mass-energy equivalencemass-energyE=mc²**

:Using Einstein's mass-energy equivalence,

When an object is pushed in the direction of motion, it gains momentum and energy, but when the object is already traveling near the speed of light, it cannot move much faster, no matter how much energy it absorbs.

### Kinetic energy

**kinetickinetic energiesenergy**

Another property of the motion, kinetic energy, must be known.

The kinetic energy of an object is related to its momentum by the equation:

### Uncertainty principle

**Heisenberg uncertainty principleHeisenberg's uncertainty principleuncertainty relation**

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

In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables or canonically conjugate variables such as position x and momentum p, can be known or, depending on interpretation, to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value.