Turn (angle)
Unit of plane angle where a full circle equals 1 / From Wikipedia, the free encyclopedia
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The turn (symbol tr or pla) is a unit of plane angle measurement equal to 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).[lower-alpha 1] 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.
It has been suggested that Draft:Tau (mathematical constant) be merged into this article. (Discuss) Proposed since July 2024. |
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 |
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. (See below for the formula.) Subdivisions of a turn include half-turns and quarter-turns, spanning a straight angle and a right angle, respectively; metric prefixes can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc.
Another common unit for representing angles is radians, which are usually stated in terms of (pi). The symbol , as representing one half-turn, was developed by William Jones in 1706 and then popularized by Leonhard Euler.[3][4] In 2010, Michael Hartl proposed instead using the symbol (tau), equal to and corresponding to one turn, for greater conceptual simplicity.[5] This proposal did not initially gain widespread acceptance in the mathematical community,[6] but the constant has become more widespread,[7] having been added to several major programming languages and calculators.