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    In diesen Phasen ist das Momentum auf Ihrer Seite. Sie scheinen nichts falsch machen zu können, Vorhaben gelingen wie von selbst und ein. Momentum (sächlich, lateinisch mōmentum, „Dauer einer Bewegung“) steht für: die englische Bezeichnung der physikalischen Größe Impuls · Momentum. Das Momentum ist eine wichtige Größe der technischen Analyse. Es gibt Aufschluss über Tempo und Kraft von Kursbewegungen sowie über. momentum (Latein). Wortart: Substantiv, (sächlich). Silbentrennung. Wortbedeutung/Definition: 1) die innewohnende Kraft zur. Worttrennung: Genitiv: Bedeutungen: [1] die innewohnende Kraft zur Bewegung​: [2] die etwas anderes bewegende Kraft: [3] bildlich: der entscheidende.

    Das Momentum

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    Now if a given coordinate q i does not appear in the Lagrangian although its time derivative might appear , then. This is the generalization of the conservation of momentum.

    Even if the generalized coordinates are just the ordinary spatial coordinates, the conjugate momenta are not necessarily the ordinary momentum coordinates.

    An example is found in the section on electromagnetism. In Hamiltonian mechanics , the Lagrangian a function of generalized coordinates and their derivatives is replaced by a Hamiltonian that is a function of generalized coordinates and momentum.

    The Hamiltonian is defined as. The Hamiltonian equations of motion are [29]. As in Lagrangian mechanics, if a generalized coordinate does not appear in the Hamiltonian, its conjugate momentum component is conserved.

    Conservation of momentum is a mathematical consequence of the homogeneity shift symmetry of space position in space is the canonical conjugate quantity to momentum.

    That is, conservation of momentum is a consequence of the fact that the laws of physics do not depend on position; this is a special case of Noether's theorem.

    In Maxwell's equations , the forces between particles are mediated by electric and magnetic fields.

    The electromagnetic force Lorentz force on a particle with charge q due to a combination of electric field E and magnetic field B is.

    These quantities form a four-vector, so the analogy is consistent; besides, the concept of potential momentum is important in explaining the so-called hidden-momentum of the electromagnetic fields [36].

    In Newtonian mechanics, the law of conservation of momentum can be derived from the law of action and reaction , which states that every force has a reciprocating equal and opposite force.

    Under some circumstances, moving charged particles can exert forces on each other in non-opposite directions. The Lorentz force imparts a momentum to the particle, so by Newton's second law the particle must impart a momentum to the electromagnetic fields.

    The momentum density is proportional to the Poynting vector S which gives the directional rate of energy transfer per unit area: [38] [39].

    If momentum is to be conserved over the volume V over a region Q , changes in the momentum of matter through the Lorentz force must be balanced by changes in the momentum of the electromagnetic field and outflow of momentum.

    If P mech is the momentum of all the particles in Q , and the particles are treated as a continuum, then Newton's second law gives.

    The quantity T ij is called the Maxwell stress tensor , defined as. The above results are for the microscopic Maxwell equations, applicable to electromagnetic forces in a vacuum or on a very small scale in media.

    It is more difficult to define momentum density in media because the division into electromagnetic and mechanical is arbitrary.

    The definition of electromagnetic momentum density is modified to. The electromagnetic stress tensor depends on the properties of the media.

    In quantum mechanics , momentum is defined as a self-adjoint operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once.

    In quantum mechanics, position and momentum are conjugate variables. This is a commonly encountered form of the momentum operator, though the momentum operator in other bases can take other forms.

    For example, in momentum space the momentum operator is represented as. Electromagnetic radiation including visible light , ultraviolet light, and radio waves is carried by photons.

    Even though photons the particle aspect of light have no mass, they still carry momentum. This leads to applications such as the solar sail.

    The calculation of the momentum of light within dielectric media is somewhat controversial see Abraham—Minkowski controversy.

    In fields such as fluid dynamics and solid mechanics , it is not feasible to follow the motion of individual atoms or molecules. Instead, the materials must be approximated by a continuum in which there is a particle or fluid parcel at each point that is assigned the average of the properties of atoms in a small region nearby.

    Consider a column of water in hydrostatic equilibrium. All the forces on the water are in balance and the water is motionless. On any given drop of water, two forces are balanced.

    The first is gravity, which acts directly on each atom and molecule inside. The second force is the sum of all the forces exerted on its surface by the surrounding water.

    The force from below is greater than the force from above by just the amount needed to balance gravity. The normal force per unit area is the pressure p.

    The average force per unit volume inside the droplet is the gradient of the pressure, so the force balance equation is [44]. If the forces are not balanced, the droplet accelerates.

    Instead, the material derivative is needed: [45]. Applied to any physical quantity, the material derivative includes the rate of change at a point and the changes due to advection as fluid is carried past the point.

    This is equal to the net force on the droplet. Forces that can change the momentum of a droplet include the gradient of the pressure and gravity, as above.

    In addition, surface forces can deform the droplet. Such a shear stress occurs if the fluid has a velocity gradient because the fluid is moving faster on one side than another.

    If the speed in the x direction varies with z , the tangential force in direction x per unit area normal to the z direction is.

    This is also a flux , or flow per unit area, of x-momentum through the surface. Including the effect of viscosity, the momentum balance equations for the incompressible flow of a Newtonian fluid are.

    These are known as the Navier—Stokes equations. The momentum balance equations can be extended to more general materials, including solids. The local conservation of momentum is expressed by the Cauchy momentum equation :.

    The Cauchy momentum equation is broadly applicable to deformations of solids and liquids. The relationship between the stresses and the strain rate depends on the properties of the material see Types of viscosity.

    A disturbance in a medium gives rise to oscillations, or waves , that propagate away from their source. In a fluid, small changes in pressure p can often be described by the acoustic wave equation :.

    In a solid, similar equations can be obtained for propagation of pressure P-waves and shear S-waves.

    In the linear approximation that leads to the above acoustic equation, the time average of this flux is zero. However, nonlinear effects can give rise to a nonzero average.

    In about AD, working in Alexandria, Byzantine philosopher John Philoponus developed a concept of momentum in his commentary to Aristotle 's Physics.

    Aristotle claimed that everything that is moving must be kept moving by something. For example, a thrown ball must be kept moving by motions of the air.

    Most writers continued to accept Aristotle's theory until the time of Galileo, but a few were skeptical. Philoponus pointed out the absurdity in Aristotle's claim that motion of an object is promoted by the same air that is resisting its passage.

    He proposed instead that an impetus was imparted to the object in the act of throwing it. He agreed that an impetus is imparted to a projectile by the thrower; but unlike Philoponus, who believed that it was a temporary virtue that would decline even in a vacuum, he viewed it as a persistent, requiring external forces such as air resistance to dissipate it.

    Buridan, who in about was made rector of the University of Paris, referred to impetus being proportional to the weight times the speed.

    Moreover, Buridan's theory was different from his predecessor's in that he did not consider impetus to be self-dissipating, asserting that a body would be arrested by the forces of air resistance and gravity which might be opposing its impetus.

    This should not be read as a statement of the modern law of momentum, since he had no concept of mass as distinct from weight and size, and more important, he believed that it is speed rather than velocity that is conserved.

    So for Descartes if a moving object were to bounce off a surface, changing its direction but not its speed, there would be no change in its quantity of motion.

    Leibniz , in his " Discourse on Metaphysics ", gave an argument against Descartes' construction of the conservation of the "quantity of motion" using an example of dropping blocks of different sizes different distances.

    He points out that force is conserved but quantity of motion, construed as the product of size and speed of an object, is not conserved. Christiaan Huygens concluded quite early that Descartes's laws for the elastic collision of two bodies must be wrong, and he formulated the correct laws.

    The war ended in , and Huygens announced his results to the Royal Society in The first correct statement of the law of conservation of momentum was by English mathematician John Wallis in his work, Mechanica sive De Motu, Tractatus Geometricus : "the initial state of the body, either of rest or of motion, will persist" and "If the force is greater than the resistance, motion will result".

    His Definition II defines quantitas motus , "quantity of motion", as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum.

    From Wikipedia, the free encyclopedia. This article is about linear momentum. It is not to be confused with angular momentum. This article is about momentum in physics.

    For other uses, see Momentum disambiguation. Conserved physical quantity related to the motion of a body. Momentum of a pool cue ball is transferred to the racked balls after collision.

    Second law of motion. History Timeline Textbooks. Newton's laws of motion. Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton—Jacobi equation Appell's equation of motion Koopman—von Neumann mechanics.

    Core topics. Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed.

    Main article: Conservation of momentum. Main article: Elastic collision. Main article: Inelastic collision. See also: Variable-mass system.

    See also: Mass in special relativity and Tests of relativistic energy and momentum. Main article: Four-momentum. See also: Analytical mechanics.

    Further information: Momentum operator. Main article: Cauchy momentum equation. This section needs attention from an expert in History of Science.

    The specific problem is: Dispute over originator of conservation of momentum. See the talk page for details. WikiProject History of Science may be able to help recruit an expert.

    November See also: Theory of impetus. Physics portal. Crystal momentum Galilean cannon Momentum transfer Newton's cradle Planck momentum Position and momentum space.

    Archived from the original on Retrieved Engineering Mechanics, An Introduction to Dynamics 3rd ed. PWS Publishing Company.

    Invitation to Contemporary Physics illustrated ed. World Scientific. Archived from the original on 18 August Retrieved 2 August Verflixt und zugenäht!

    Herkunft und Funktion des Ausrufezeichens. Vorvergangenheit in der indirekten Rede. Wann kann der Bindestrich gebraucht werden?

    Was ist ein Twitter-Roman? Anglizismus des Jahres. Wort und Unwort des Jahres in Deutschland. Wort und Unwort des Jahres in Liechtenstein.

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