Editing Angular frequency (section)

{{Short description|Rate of change of angle}}
{{Infobox physical quantity
| name = Angular frequency
| othernames = angular speed, angular rate
| width =
| background =
| image = File:AngularFrequency.gif
| caption = {{longitem|Angular speed [[omega|''ω'']] is greater than rotational frequency [[nu (letter)|''ν'']] by a factor of 2{{pi}}.}}
| unit = [[radian per second]] (rad/s)
| otherunits = [[degrees per second]] (°/s)
| symbols = ω
| baseunits = [[Inverse second|s<sup>−1</sup>]]
| derivations = ''ω''{{=}}2{{pi}}{{nbsp}}rad{{sdot}}''ν'', ''ω''{{=}}d''θ''/d''t''
| dimension = wikidata
| extensive =
| intensive =
| conserved =
| transformsas =
}}
[[File:Rotating Sphere.gif|right|thumb|A sphere rotating around an axis. Points farther from the axis move faster, satisfying {{nowrap|1=''ω'' = ''v'' / ''r''}}.]]

In [[physics]], '''angular frequency''' (symbol '''''ω'''''), also called '''angular speed''' and '''angular rate''', is a [[Scalar (physics)|scalar]] measure of the [[angle]] [[Rate (mathematics)|rate]] (the angle per unit time) or the [[temporal rate of change]] of the [[phase (waves)|phase]] [[function argument|argument]] of a [[sinusoidal waveform]] or [[sine function]] (for example, in oscillations and waves).
Angular frequency (or angular speed) is the magnitude of the [[pseudovector]] quantity ''[[angular velocity]]''.<ref name="UP1">
{{cite book
  | last1 = Cummings | first1 = Karen
  | last2 = Halliday | first2 = David
  | title = Understanding physics
  | publisher = John Wiley & Sons, authorized reprint to Wiley – India
  | date = 2007
  | location = New Delhi
  | pages = 449, 484, 485, 487
  | url = https://books.google.com/books?id=rAfF_X9cE0EC
  | isbn =978-81-265-0882-2
}}(UP1)</ref>

Angular frequency can be obtained multiplying ''[[rotational frequency]]'', ''ν'' (or ordinary ''[[frequency]]'', ''f'') by a full [[turn (unit)|turn]] (2[[Pi|{{pi}}]] [[radians]]): {{nowrap|1=''ω'' = 2{{pi}} rad⋅''ν''}}.
It can also be formulated as {{nowrap|1=''ω'' = d''θ''/d''t''}}, the [[instantaneous rate of change]] of the [[angular displacement]], ''θ'', with respect to time,&nbsp;''t''.<ref name="ISO80000-3_2019">{{cite web |title=ISO 80000-3:2019 Quantities and units — Part 3: Space and time |publisher=[[International Organization for Standardization]] |date=2019 |edition=2 |url=https://www.iso.org/standard/64974.html |access-date=2019-10-23}} [https://www.iso.org/obp/ui/#iso:std:iso:80000:-3:ed-2:v1:en] (11 pages)</ref><ref>
{{cite book
  | last = Holzner
  | first = Steven
  | title = Physics for Dummies
  | publisher = Wiley Publishing
  | date= 2006
  | location = Hoboken, New Jersey
  | pages = [https://archive.org/details/physicsfordummie00holz/page/201 201]
  | url = https://archive.org/details/physicsfordummie00holz
  | url-access = registration
  | quote = angular frequency.
  | isbn =978-0-7645-5433-9
}}</ref>