Momentum

The physical size of the pulse, referred to as a movement amount or movement quantity describing the movement of a mass body affected. Clearly corresponds to the pulse about the " force " which occurs, for example to light in a traffic accident between trucks and cars.

The pulse is like the speed associated with it a vector quantity, so it has a magnitude and points in the direction of the movement. Its particular importance lies in the fact that it is a conserved quantity (see Section momentum conservation ). Each movable body can its momentum to take over as in a collision process, in whole or in part to another body or other bodies. Also, fields can be transferred to other particles by force effect pulse of a particle.

Remarks Designation and unit

In the International System of Units, there is no separate unit for the pulse, is used N · s = kg · m · s -1.

In English, the pulse is called momentum. In contrast, the English impulse refers to the change of momentum within a certain time, so the impulse (see Section impulse ).

Definition, correlations with mass and energy

Classical Mechanics

In Newtonian mechanics the momentum and velocity are linked by the mass of the body:

Since the mass is a scalar, momentum and velocity are vectors with the same direction.

In addition, can form between momentum, mass and kinetic energy following relationship:

To change the speed of a body, a pulse has to be transmitted. The time per transmitted pulse is the power:

Electrically charged particles

Become an electrically charged particles set to the ground by an electric field in motion, the kinetic energy is obtained from the product of charge and potential difference:

The momentum of the particle is then:

Special Theory of Relativity

In relativistic physics, the pulse of a body is connected with its speed non-linearly combined (the speed of light):

With the mass and energy

Is the energy - momentum relation

While in classical physics, every body has a nonzero mass, the relativistic energy - momentum relation for massless particles like photons is considered. Always move with the speed of light. When the magnitude of the photon momentum of its wavelength λ depends on:

Where the Planck constant is. The energy of a photon is up to a factor equal to the magnitude of its momentum:

The energy and momentum, the notice against each moving observer in a body to go through a Lorentz transformation apart out.

The notified in accordance with the energy density of momentum density of the electromagnetic field is the cross product of the electric and magnetic field

Multiplied with this is the energy flux density of the Poynting vector. Integrating the pulse density of a volume, to give the pulse of the electromagnetic field in said volume.

Conservation of momentum

The momentum is conserved, because in a closed system (more precisely, concluded inertial frame ) is the total momentum, the sum of all individual pulses occurring in the system is constant.

Thus, the total initial momentum is equal to the vector sum of the existing at any time hereafter individual pulses. Collisions and other processes in which to change the speeds, always end so that this principle is not violated (see kinematics ( Teilchenprozesse ) ).

When inelastic collision, kinetic energy is lost by plastic deformation, but the momentum conservation law is the conservation of energy -independent and applies to both elastic and inelastic collisions with.

Impulse

From the force on a body and its duration of action results in a change in momentum, which is called impulse. Both the magnitude and the direction of the force play a role. The impulse is often denoted by the symbols, its SI unit is 1 N · s

Is the force constant in the time interval, the impulse can be calculated by the following equation:

However, is not constant, you can either expect a mean force or, if it is known, determine the force impact by integrating:

Pulse in the Lagrangian and Hamiltonian formalism

In the Lagrangian and Hamiltonian formalism of generalized impulse is introduced; the three components of the momentum vector belong to the generalized impulse; but also, for example, the angular momentum.

In the Hamiltonian formalism in quantum mechanics, momentum is the place for canonically conjugate variables. The (generalized ) momentum is referred to in this context as the canonical momentum. The possible pairs of spatial coordinates and canonical pulses of a physical system form the phase space in Hamiltonian mechanics.

Magnetic fields in the canonical momentum of a charged particle contains an additional term which is related to the vector potential of the B- field in the context (see Generalized pulse).

Pulse in flowing media

For continuously distributed mass, such as in fluid mechanics, contains a small area around the point mass case is the volume of the area. is the mass density at the site. It may change with time.

The momentum in this area is mass times velocity. Mass density times velocity so the momentum density.

The continuity equation

States that the momentum in a small area can change only in that unbalanced pulse current flows into and out of the area and that a force acts.

Here, the first term on the left side is the change in the pulse density with time, and the second term describes the spatial variation of the pulse current. The right side is the force element acting on the volume density; For example, the gradient of the pressure or weight.

See also the Navier -Stokes equations

Momentum in quantum mechanics

In quantum mechanics, a physical condition is usually no exact pulse. It can only be given the probability that the pulse in this or that of a particle range. The same applies for the place. For pulse and place the Heisenberg uncertainty principle, according to which a particle can not simultaneously have an accurate pulse and a precise location applies.

Eigenstates of the momentum operator are plane waves with wavelength

Where the Planck constant is. The de Broglie wavelength of matter waves of free particles is thus determined by the momentum. It should be noted that the pulse of the canonical momentum, which is usually not the kinetic momentum corresponds in quantum mechanics.