What is momentum?

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What is momentum?

Answer 1

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Momentum     · Physics

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This article is about momentum in physics. For other uses, see Momentum (disambiguation).

Classical mechanics

Newton's Second Law

History of ... [hide]Fundamental concepts

Space · Time · Mass · Force

Energy · Momentum



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Newtonian mechanics

Lagrangian mechanics

Hamiltonian mechanics



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Applied mechanics

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Galileo[citation needed] · Kepler[citation needed] · Newton

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Title page of the 1st edition of Newton's work defining the laws of motion.In classical mechanics, momentum (pl. momenta; SI unit kg·m/s, or, equivalently, N·s) is the product of the mass and velocity of an object (p = mv). For more accurate measures of momentum, see the section "modern definitions of momentum" on this page. It is sometimes referred to as linear momentum to distinguish it from the related subject of angular momentum. Linear momentum is a vector quantity, since it has a direction as well as a magnitude. Angular momentum is a pseudovector quantity because it gains an additional sign flip under an improper rotation. The total momentum of any group of objects remains the same unless outside forces act on the objects.

Momentum is a conserved quantity, meaning that the total momentum of any closed system (one not affected by external forces) cannot change.

Contents [hide]

1 History of the concept

2 Linear momentum of a particle

3 Linear momentum of a system of particles

3.1 Relating to mass and velocity

3.2 Relating to force- General equations of motion

4 Conservation of linear momentum

4.1 Elastic collisions

4.1.1 Head-on collision (1 dimensional)

4.1.2 Multi-dimensional collisions

4.2 Inelastic collisions

4.3 Explosions

5 Modern definitions of momentum

5.1 Momentum in relativistic mechanics

5.2 Momentum in quantum mechanics

5.3 Momentum in electromagnetism

6 See also

7 Notes

8 References

9 External links



[edit] History of the concept

The word for the general concept of mōmentum was used in the Roman Republic primarily to mean "a movement, motion (as an indwelling force ...)." A fish was able to change velocity (velocitas) through the mōmentum of its tail.[1] The word is formed by an accretion of suffices on the stem of Latin movēre, "to move." A movi-men- is the result of the movēre just as frag-men- is the result of frangere, "to break." Extension by -to- obtains mōvimentum and fragmentum, the former contracting to mōmentum.[2]

The mōmentum was not merely the motion, which was mōtus, but was the power residing in a moving object, captured by today's mathematical definitions. A mōtus, "movement", was a stage in any sort of change,[3] while velocitas, "swiftness", captured only speed. The Romans, due to limitations inherent in the Roman numeral system,[clarify] were unable to go further with the perception.[citation needed]

The concept of momentum in classical mechanics was originated by a number of great thinkers and experimentalists. The first of these was Ibn Sina (Avicenna) circa 1000, who referred to impetus as proportional to weight times velocity.[4] René Descartes later referred to mass times velocity as the fundamental force of motion. Galileo in his Two New Sciences used the Italian word "impeto."

The question has been much debated as to what Sir Isaac Newton's contribution to the concept was. Apparently nothing, except to state more fully and with better mathematics what was already known. The first and second of Newton's Laws of Motion had already been stated by John Wallis in his 1670 work, Mechanica slive 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...."[5] Wallis uses momentum and vis for force.

Newton's "Mathematical Principles of Natural History" when it first came out in 1686 showed a similar casting around for words to use for the mathematical momentum. His Definition II[6] defines quantitas motus, "quantity of motion," as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum.[7] Thus when in Law II he refers to mutatio motus, "change of motion," being proportional to the force impressed, he is generally taken to mean momentum and not motion.[8]

It remained only to assign a standard term to the quantity of motion. The first use of "momentum" in its proper mathematical sense is not clear but by the time of Jenning's Miscellanea in 1721, four years before the final edition of Newton's Principia Mathematica, momentum M or "quantity of motion" was being defined for students as "a rectangle", the product of Q and V where Q is "quantity of material" and V is "velocity", s/t.[9]

[edit] Linear momentum of a particle



Newton's apple in Einstein's elevator, a frame of reference. In it the apple has no velocity or momentum; outside, it does.If an object is moving in any reference frame, then it has momentum in that frame. It is important to note that momentum is frame dependent. That is, the same object may have a certain momentum in one frame of reference, but a different amount in another frame. For example, a moving object has momentum in a reference frame fixed to a spot on the ground, while at the same time having 0 momentum in a reference frame attached to the object's center of mass.

The amount of momentum that an object has depends on two physical quantities: the mass and the velocity of the moving object in the frame of reference. In physics, the usual symbol for momentum is a small bold p (bold because it is a vector); so this can be written:



where:

is the momentum

is the mass

the velocity

Example: a model airplane of 1 kg travelling due north at 1 m/s in straight and level flight has a momentum of 1 kg m/s due north measured from the ground. To the dummy pilot in the cockpit it has a velocity and momentum of zero.

According to Newton's second law the rate of change of the momentum of a particle is proportional to the resultant force acting on the particle and is in the direction of that force. In the case of constant mass, and velocities much less than the speed of light, this definition results in the equation



or just simply



where F is understood to be the resultant.

Example: a model airplane of 1 kg accelerates from rest to a velocity of 1 m/s due north in 1 sec. The thrust required to produce this acceleration is 1 newton. The change in momentum is 1 kg-m/sec. To the dummy pilot in the cockpit there is no change of momentum. Its pressing backward in the seat is a reaction to the unbalanced thrust, shortly to be balanced by the drag.

[edit] Linear momentum of a system of particles

[edit] Relating to mass and velocity

The linear momentum of a system of particles is the vector sum of the momenta of all the individual objects in the system.



where

is the momentum of the particle system

is the mass of object i

the vector velocity of object i

is the number of objects in the system

It can be shown that, in the center of mass frame the momentum of a system is zero. Additionally, the momentum in a frame of reference that is moving at a velocity vcm with respect to that frame is simply:



where:

.

[edit] Relating to force- General equations of motion



Motion of a material bodyThe linear momentum of a system of particles can also be defined as the product of the total mass  of the system times the velocity of the center of mass



This is commonly known as Newton's second law.

For a more general derivation using tensors, we consider a moving body (see Figure), assumed as a continuum, occupying a volume  at a time , having a surface area , with defined traction or surface forces  acting on every point of the body surface, body forces  per unit of volume on every point within the volume , and a velocity field  prescribed throughout the body. Following the previous equation, The linear momentum of the system is:



By definition the stress vector is , then



Using the Gauss's divergency theorem to convert a surface integral to a volume integral gives





For an arbitrary volume the integrand itself must be zero, and we have the Cauchy's equation of motion



If a system is in equilibrium, the change in momentum with respect to time is equal to 0, as there is no acceleration.



or using tensors,



These are the equilibrium equations which are used in solid mechanics for solving problems of linear elasticity. In engineering notation, the equilibrium equations are expressed in Cartesian coordinates as







[edit] Conservation of linear momentum

The law of conservation of linear momentum is a fundamental law of nature, and it states that the total momentum of a closed system of objects (which has no interactions with external agents) is constant. One of the consequences of this is that the center of mass of any system of objects will always continue with the same velocity unless acted on by a force from outside the system.

Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate quantity to momentum). So, momentum conservation can be philosophically stated as "nothing depends on location per se".

In an isolated system (one where external forces are a

Answer 2

momentum is the result of forces acting on objects with mass; produced in beta decay.

you can look it up if you want!

Answer 3

momentum = mass * velocity

Answer 4

mv

Answer 5

The mass of an object multiplied by its velocity.(Velocity=speed: distance travelled per unit time)

(Mass=the property of a body that causes it to have weight in a gravitational field)

So, momentum is how fast the object is X its weight.