Editing Rotational frequency (section)

{{Short description|Number of rotations per unit time}}
{{Distinguish|Circular motion}}
{{redirect|Rotation speed|the speed at which aircraft begin to [[Rotation (aeronautics)|rotate]]|V speeds#Regulatory V-speeds}}
{{Infobox Physical quantity
|bgcolour=
|image = File:AngularFrequency.gif
|caption = {{longitem|Angular speed ''[[omega|ω]]'' (in radians per second), is greater than rotational frequency ''[[nu (letter)|ν]]'' (in [[Hertz|Hz]]), by a factor of 2π.}}
|name=Rotational frequency
|othernames=rotational speed, rate of rotation
|symbols=<math>\nu</math>, ''n''
|unit=[[hertz|Hz]]
|otherunits=[[rotations per minute|rpm]], [[Cycles per second|cps]]
|baseunits=[[Reciprocal seconds|s<sup>−1</sup>]]
|dimension=wikidata
|derivations=''ν''{{=}}ω/(2π{{nbsp}}rad), ''n''{{=}}d''N''/d''t''
}}
{{Classical mechanics|rotational}}

'''Rotational frequency''', also known as '''rotational speed''' or '''rate of rotation''' (symbols ''ν'', lowercase Greek [[Nu (letter)|nu]], and also ''n''), is the [[frequency]] of [[rotation]] of an object [[Rotation around a fixed axis|around an axis]].
Its [[SI unit]] is the [[reciprocal second]]s (s<sup>−1</sup>); other common [[units of measurement]] include the [[hertz]] (Hz), [[cycles per second]] (cps), and [[revolutions per minute]] (rpm).<ref>{{Cite book
|last1=Atkins
|first1=Tony
|last2=Escudier
|first2=Marcel
|title=A Dictionary of Mechanical Engineering
|year=2013
|url=http://www.oxfordreference.com/view/10.1093/acref/9780199587438.001.0001/acref-9780199587438-e-5953?rskey=EBYJmx&result=1
|publisher=Oxford University Press
|isbn=9780199587438
}}</ref>{{efn|"The rotational frequency ''n'' of a rotating body is defined to be the number of revolutions it makes in a time interval divided by that time interval [4: ISO 80000-3]. The SI unit of this quantity is thus the reciprocal second (s<sup>−1</sup>). However, as pointed out in Ref. [4: ISO 80000-3], the designations “revolutions per second” (r/s) and “revolutions per minute” (r/min) are widely used as units for rotational frequency in specifications on rotating machinery."<ref name="NISTGuide_2009"/>}}{{efn|"The SI unit of frequency is hertz, the SI unit of angular velocity and angular frequency is radian per second, and the SI unit of activity is becquerel, implying counts per second. Although it is formally correct to write all three of these units as the reciprocal second, the use of the different names emphasizes the different nature of the quantities concerned. It is especially important to carefully distinguish frequencies from angular frequencies, because by definition their numerical values differ by a factor [see ISO 80000-3 for details] of 2π. Ignoring this fact may cause an error of 2π. Note that in some countries, frequency values are conventionally expressed using “cycle/s” or “cps” instead of the SI unit Hz, although “cycle” and “cps” are not units in the SI. Note also that it is common, although not recommended, to use the term frequency for quantities expressed in rad/s. Because of this, it is recommended that quantities called “frequency”, “angular frequency”, and “angular velocity” always be given explicit units of Hz or rad/s and not s<sup>−1</sup>."<ref name="SIBrochure_9"/>}}

Rotational frequency can be obtained dividing ''[[angular frequency]]'', ω, by a full [[turn (unit)|turn]] (2[[Pi|π]] [[radians]]): ''ν''{{=}}ω/(2π{{nbsp}}rad).
It can also be formulated as the [[instantaneous rate of change]] of the [[number of rotations]], ''N'', with respect to time, ''t'': ''n''{{=}}d''N''/d''t'' (as per [[International System of Quantities]]).<ref name="ISO80000-3_2019">{{cite web |date=2019 |title=ISO 80000-3:2019 Quantities and units — Part 3: Space and time |url=https://www.iso.org/standard/64974.html |access-date=2019-10-23 |publisher=[[International Organization for Standardization]] |edition=2}} [https://www.iso.org/obp/ui/#iso:std:iso:80000:-3:ed-2:v1:en] (11 pages)</ref>
Similar to ordinary [[period (physics)|period]], the reciprocal of rotational frequency is the '''rotation period''' or '''period of rotation''', ''T''{{=}}''ν''<sup>−1</sup>{{=}}''n''<sup>−1</sup>, with dimension of time (SI unit [[seconds]]).

'''Rotational velocity''' is the [[vector quantity]] whose magnitude equals the [[Scalar (physics)|scalar]] rotational speed. In the special cases of [[spin (geometry)|''spin'']] (around an axis internal to the body) and [[revolution (geometry)|''revolution'']] (external axis), the rotation speed may be called '''''spin speed''''' and '''''revolution speed''''', respectively.

'''Rotational acceleration''' is the rate of change of rotational velocity; it has dimension of squared reciprocal time and SI units of squared reciprocal seconds (s<sup>−2</sup>); thus, it is a normalized version of ''[[angular acceleration]]'' and it is analogous to ''[[chirpyness]]''.