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In [http://en.wikipedia.org/wiki/Classical_mechanics 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). 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 [[force]]s [[act]] on the objects (law of conservation of momentum).

In [https://en.wikipedia.org/wiki/Classical_mechanics 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). 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 [[force]]s [[act]] on the objects (law of conservation of momentum).

Momentum is a conserved quantity, meaning that the total momentum of any closed [[system]] (one not affected by external forces) cannot [[change]]. This law is also true in [[special relativity]].

Momentum is a conserved quantity, meaning that the total momentum of any closed [[system]] (one not affected by external forces) cannot [[change]]. This law is also true in [[special relativity]].

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]],[1] while velocitas, "swiftness", captured only [[speed]]. The [[Romans]], handicapped by the limitations inherent in the Roman numeral system which lacks a [[symbol]] for [[zero]], took these [[ideas]] no further.

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]],[1] while velocitas, "swiftness", captured only [[speed]]. The [[Romans]], handicapped by the limitations inherent in the Roman numeral system which lacks a [[symbol]] for [[zero]], took these [[ideas]] no further.

The [[concept]] of momentum in classical [[mechanics]] was originated by a number of great [[thinkers]] and [[experiment]]alists. The first of these was Ibn Sina ([[Avicenna]]) circa 1000, during the [http://en.wikipedia.org/wiki/Islamic_Golden_Age Islamic Renaissance] who referred to impetus as proportional to weight times velocity.[2] René [[Descartes]] later referred to momentum as mass times velocity and as the fundamental [[force]] of [[motion]]. This allowed Descartes to maintain that mass and velocity are fundamental and conserved, everywhere and all the time.[3] [[Galileo]], later, in his [http://en.wikipedia.org/wiki/Two_New_Sciences Two New Sciences], used the Italian word "impeto."

The [[concept]] of momentum in classical [[mechanics]] was originated by a number of great [[thinkers]] and [[experiment]]alists. The first of these was Ibn Sina ([[Avicenna]]) circa 1000, during the [https://en.wikipedia.org/wiki/Islamic_Golden_Age Islamic Renaissance] who referred to impetus as proportional to weight times velocity.[2] René [[Descartes]] later referred to momentum as mass times velocity and as the fundamental [[force]] of [[motion]]. This allowed Descartes to maintain that mass and velocity are fundamental and conserved, everywhere and all the time.[3] [[Galileo]], later, in his [https://en.wikipedia.org/wiki/Two_New_Sciences Two New Sciences], used the Italian word "impeto."

The question has been much [[debate]]d as to what [[Isaac Newton]] contributed to the [[concept]]. The answer is apparently nothing, except to state more fully and with better [[mathematics]] what was already known. Yet for scientists, this was the death knell for Aristotelian [[physics]] and supported other progressive scientific theories (i.e., [[Kepler]]'s laws of planetary motion). Conceptually, the first and second of [http://en.wikipedia.org/wiki/Newton%27s_Laws_of_Motion Newton's Laws of Motion] had already been stated by John Wallis in his 1670 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".[4] Wallis uses momentum and vis for force.

The question has been much [[debate]]d as to what [[Isaac Newton]] contributed to the [[concept]]. The answer is apparently nothing, except to state more fully and with better [[mathematics]] what was already known. Yet for scientists, this was the death knell for Aristotelian [[physics]] and supported other progressive scientific theories (i.e., [[Kepler]]'s laws of planetary motion). Conceptually, the first and second of [https://en.wikipedia.org/wiki/Newton%27s_Laws_of_Motion Newton's Laws of Motion] had already been stated by John Wallis in his 1670 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".[4] Wallis uses momentum and vis for force.

Newton's [http://en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica Philosophiæ Naturalis Principia Mathematica], when it was first published in 1686, showed a similar casting around for [[words]] to use for the mathematical momentum. His Definition II[5] defines quantitas motus, "quantity of motion", as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum.[6] 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.[7]

Newton's [https://en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica Philosophiæ Naturalis Principia Mathematica], when it was first published in 1686, showed a similar casting around for [[words]] to use for the mathematical momentum. His Definition II[5] defines quantitas motus, "quantity of motion", as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum.[6] 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.[7]

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.[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.[8]

Some languages, such as French and Italian, still lack a single term for momentum, and use a phrase such as the literal translation of "quantity of motion".[http://en.wikipedia.org/wiki/Momentum]

Some languages, such as French and Italian, still lack a single term for momentum, and use a phrase such as the literal translation of "quantity of motion".[https://en.wikipedia.org/wiki/Momentum]

==Notes==

==Notes==

# Lewis, Charleton T.; Charles Short. "mōtus" (html). A Latin Dictionary. Tufts University: The Perseus Project. Retrieved 2008-02-15.

# Lewis, Charleton T.; Charles Short. "mōtus" (html). A Latin Dictionary. Tufts University: The Perseus Project. Retrieved 2008-02-15.

*Hand, Louis N.; Finch, Janet D.. Analytical Mechanics. Cambridge University Press. Chapter 4.

*Hand, Louis N.; Finch, Janet D.. Analytical Mechanics. Cambridge University Press. Chapter 4.

==External links==

==External links==

* [http://www.lightandmatter.com/html_books/2cl/ch04/ch04.html Conservation of momentum] - A chapter from an online textbook

* [https://www.lightandmatter.com/html_books/2cl/ch04/ch04.html Conservation of momentum] - A chapter from an online textbook

[[Category: Physics]]

[[Category: Physics]]