![]() | It has been suggested that Draft:Tau (mathematical constant) be merged into this article. (Discuss) Proposed since July 2024. |
Turn | |
---|---|
![]() Counterclockwise rotations about the center point starting from the right, where a complete rotation corresponds to an angle of rotation of 1 turn. | |
General information | |
Unit of | Plane angle |
Symbol | tr, pla, rev, cyc |
Conversions | |
1 tr in ... | ... is equal to ... |
radians | 2π rad ≈ 6.283185307... rad |
milliradians | 2000π mrad ≈ 6283.185307... mrad |
degrees | 360° |
gradians | 400g |
The turn (symbol tr or pla) is a unit of plane angle measurement that is the angular measure subtended by a complete circle at its center. It is equal to 2π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c)[1] or to one revolution (symbol rev or r).[2] Common related units of frequency are cycles per second (cps) and revolutions per minute (rpm).[a] The angular unit of the turn is useful in connection with, among other things, electromagnetic coils (e.g., transformers), rotating objects, and the winding number of curves. Subdivisions of a turn include the half-turn and quarter-turn, spanning a straight angle and a right angle, respectively; metric prefixes can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc.
Because one turn is radians, some have proposed representing 2π with a single letter. In 2010, Michael Hartl proposed using the Greek letter (tau), equal to the ratio of a circle's circumference to its radius () and corresponding to one turn, for greater conceptual simplicity when stating angles in radians.[3] This proposal did not initially gain widespread acceptance in the mathematical community,[4] but the constant has become more widespread,[5] having been added to several major programming languages and calculators.
In the ISQ, an arbitrary "number of turns" (also known as "number of revolutions" or "number of cycles") is formalized as a dimensionless quantity called rotation, defined as the ratio of a given angle and a full turn. It is represented by the symbol N.
Fitzpatrick_2021
was invoked but never defined (see the help page).IET_2016
was invoked but never defined (see the help page).Hartl_2019
was invoked but never defined (see the help page).Telegraph_2011
was invoked but never defined (see the help page).McMillan_2020
was invoked but never defined (see the help page).
Cite error: There are <ref group=lower-alpha>
tags or {{efn}}
templates on this page, but the references will not show without a {{reflist|group=lower-alpha}}
template or {{notelist}}
template (see the help page).
© MMXXIII Rich X Search. We shall prevail. All rights reserved. Rich X Search