Editing Angular displacement (section)

== Definition and units ==
Angular displacement may be expressed in [[radian]]s or degrees. Using radians provides a very simple relationship between distance traveled around the circle (''[[circular arc]] [[arc length|length]]'') and the distance ''r'' from the centre (''[[radius]]''):

:<math>\theta = \frac{s}{r} \mathrm{rad}</math>

For example, if a body rotates 360° around a circle of radius ''r'', the angular displacement is given by the distance traveled around the circumference - which is 2π''r'' - divided by the radius: <math>\theta= \frac{2\pi r}r</math> which easily simplifies to: <math>\theta=2\pi</math>. Therefore, 1 [[revolution (unit)|revolution]] is <math>2\pi</math> radians.

The above definition is part of the [[International System of Quantities]] (ISQ), formalized in the international standard [[ISO 80000-3]] (Space and time),<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> and adopted in the [[International System of Units]] (SI).<ref name="SIBrochure_9">{{SIbrochure9th}}</ref><ref name="NISTGuide_2009">{{cite web |title=The NIST Guide for the Use of the International System of Units, Special Publication 811 |author-first1=Ambler |author-last1=Thompson |author-first2=Barry N. |author-last2=Taylor |edition=2008 |publisher=[[National Institute of Standards and Technology]] |date=2020-03-04 |orig-date=2009-07-02 |ref={{sfnref|NIST|2009}} |url=https://www.nist.gov/pml/special-publication-811 |access-date=2023-07-17}} [https://web.archive.org/web/20230515201622/https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication811e2008.pdf]</ref>

Angular displacement may be signed, indicating the sense of rotation (e.g., [[clockwise]]);<ref name="ISO80000-3_2019"/> it may also be greater (in [[absolute value]]) than a full [[turn (angle)|turn]].
In the ISQ/SI, angular displacement is used to define the ''[[number of revolutions]]'', ''N''{{=}}θ/(2π rad), a ratio-type [[quantity of dimension one]].