Editing Angular momentum (section)

{{Short description|Conserved physical quantity; rotational analogue of linear momentum}}
{{Infobox physical quantity
| name = Angular momentum
| image = Gyroskop.jpg
| caption = This [[gyroscope]] remains upright while spinning owing to the conservation of its angular momentum.
| unit =
| otherunits =
| symbols = {{math|'''L'''}}
| baseunits = kg⋅m<sup>2</sup>⋅s<sup>−1</sup>
| dimension = wikidata
| extensive =
| intensive =
| conserved = yes
| transformsas =
| derivations = {{math|1='''L''' = ''I'''ω''''' = '''r''' × '''p'''}}
}}
{{Classical mechanics|cTopic=Fundamental concepts}}

'''Angular momentum''' (sometimes called '''moment of momentum''' or '''rotational momentum''') is the [[rotational]] analog of [[Momentum|linear momentum]]. It is an important [[physical quantity]] because it is a [[Conservation law|conserved quantity]]&nbsp;– the total angular momentum of a [[closed system]] remains constant.  Angular momentum has both a [[direction (geometry)|direction]] and a magnitude, and both are conserved.  [[Bicycle and motorcycle dynamics|Bicycles and motorcycles]], [[flying disc]]s,<ref>{{cite web |url=https://www.scientificamerican.com/article/bring-science-home-frisbee-aerodynamics/ |title=Soaring Science: The Aerodynamics of Flying a Frisbee |last1= |first1= |last2= |first2= |date=August 9, 2012 |website= |publisher=Scientific American |accessdate=January 4, 2022}}</ref> [[Rifling|rifled bullets]], and [[gyroscope]]s owe their useful properties to conservation of angular momentum.  Conservation of angular momentum is also why [[hurricane]]s<ref name="Tropical Cyclone Structure">{{cite web |url=https://www.weather.gov/jetstream/tc_structure |title=Tropical Cyclone Structure |last1= |first1= |last2= |first2= |date= |website= |publisher=National Weather Service |accessdate=January 4, 2022}}</ref> form spirals and [[neutron star]]s have high rotational rates.  In general, conservation limits the possible motion of a system, but it does not uniquely determine it.

The three-dimensional angular momentum for a [[point particle]] is classically represented as a [[pseudovector]] {{math|'''r''' × '''p'''}}, the [[cross product]] of the particle's [[position vector]] {{math|'''r'''}} (relative to some origin) and its [[momentum vector]]; the latter is {{math|1='''p''' = ''m'''''v'''}} in [[Newtonian mechanics]]. Unlike linear momentum, angular momentum depends on where this origin is chosen, since the particle's position is measured from it.

Angular momentum is an [[Intensive and extensive properties|extensive quantity]]; that is, the total angular momentum of any composite system is the sum of the angular momenta of its constituent parts. For a [[Continuum mechanics|continuous]]&nbsp;[[rigid body]] or a [[fluid]], the total angular momentum is the [[volume integral]] of angular momentum density (angular momentum per unit volume in the limit as volume shrinks to zero) over the entire body.

Similar to conservation of linear momentum, where it is conserved if there is no external force, angular momentum is conserved if there is no external [[torque]].  Torque can be defined as the rate of change of angular momentum, analogous to [[force]]. The net ''external'' torque on any system is always equal to the ''total'' torque on the system; the sum of all internal torques of any system is always 0 (this is the rotational analogue of [[Newton's third law of motion]]). Therefore, for a [[closed system]] (where there is no net external torque), the ''total'' torque on the system must be 0, which means that the total angular momentum of the system is constant.

The change in angular momentum for a particular interaction is called '''angular impulse''', sometimes '''twirl'''.<ref>{{cite book |year=2016|last1=Moore |first1=Thomas |title=Six Ideas That Shaped Physics, Unit C: Conservation Laws Constrain Interactions |publisher=McGraw-Hill Education |isbn=978-0-07-351394-2 |page=91 |edition=Third}}</ref> Angular impulse is the angular analog of (linear) [[Impulse (physics)|impulse]].