Turn (angle)

The turn (symbol tr or pla) is a unit of plane angle measurement that is the measure of a complete angle—the angle subtended by a complete circle at its center. One turn 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). 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. Divisions 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.

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.

Because one turn is ${\displaystyle 2\pi }$ radians, some have proposed representing ${\displaystyle 2\pi }$ with the single letter 𝜏 (tau).^[3]

There are several unit symbols for the turn.

Muchas unidades angulares se definen como una división del giro. Por ejemplo, el grado se define de tal manera que un giro equivale a 360 grados.

Utilizando prefijos métricos , el giro se puede dividir en 100 centiturns o1000 milivueltas, donde cada milivuelta corresponde a un ángulo de 0,36°, que también se puede escribir como 21′  36″ . ^{[ 14 ] [ 15 ]} Un transportador dividido en centivueltas se denomina normalmente " transportador de porcentaje ". Si bien los transportadores de porcentaje existen desde 1922, ^{[ 16 ]} los términos centivueltas, milivueltas y microvueltas fueron introducidos mucho más tarde por el astrónomo británico Fred Hoyle en 1962. ^{[ 14 ] [ 15 ]} Algunos dispositivos de medición para artillería y observación de satélites llevan escalas de milivueltas. ^{[ 17 ] [ 18 ]}

También se utilizan fracciones binarias de un giro . Los marineros tradicionalmente han dividido un giro en 32 puntos cardinales , que implícitamente tienen una separación angular de 1/32 giro  . El grado binario , también conocido como radián binario ( o brad ), es 1/256 giro. [ 19 ^{] El} grado binario se utiliza en computación para que un ángulo pueda representarse con la máxima precisión posible en un solo byte . ^Otras medidas de ángulo utilizadas en computación pueden basarse en dividir un giro completo en 2n ^partes iguales para otros valores de n . ^{[ 20 ]} 

Un turno es igual a${\displaystyle 2\pi }$=${\displaystyle \tau }$≈6,283 185 307 179 586 ^{[ 21 ]} radianes , 360 grados , o 400 grados .

En el Sistema Internacional de Cantidades (SIQ), la rotación (símbolo N ) es una magnitud física definida como el número de revoluciones : ^{[ 22 ]}

N es el número (no necesariamente un número entero) de revoluciones, por ejemplo, de un cuerpo que gira alrededor de un eje dado. Su valor viene dado por:

${\displaystyle N={\frac {\varphi }{2\pi {\text{ rad}}}}}$

where 𝜑 denotes the measure of rotational displacement.

The above definition is part of the ISQ, formalized in the international standard ISO 80000-3 (Space and time),^[22] and adopted in the International System of Units (SI).^[23][24]

Rotation count or number of revolutions is a quantity of dimension one, resulting from a ratio of angular displacement. It can be negative and also greater than 1 in modulus. The relationship between quantity rotation, N, and unit turns, tr, can be expressed as:

${\displaystyle N={\frac {\varphi }{\text{tr}}}=\{\varphi \}_{\text{tr}}}$

where {𝜑}_tr is the numerical value of the angle 𝜑 in units of turns (see Physical quantity § Components).

In the ISQ/SI, rotation is used to derive rotational frequency (the rate of change of rotation with respect to time), denoted by n:

${\displaystyle n={\frac {\mathrm {d} N}{\mathrm {d} t}}}$

The SI unit of rotational frequency is the reciprocal second (s⁻¹). Common related units of frequency are hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).

The superseded version ISO 80000-3:2006 defined "revolution" as a special name for the dimensionless unit "one",^[a] which also received other special names, such as the radian.^[b] Despite their dimensional homogeneity, these two specially named dimensionless units are applicable for non-comparable kinds of quantity: rotation and angle, respectively.^[26] "Cycle" is also mentioned in ISO 80000-3, in the definition of period.^[c]

• Ampere-turn
• Hertz (modern) or Cycle per second (older)
• Angle of rotation
• Revolutions per minute
• Repeating circle
• Spat (angular unit) – the solid angle counterpart of the turn, equivalent to 4π steradians.
• Unit interval
• Divine Proportions: Rational Trigonometry to Universal Geometry
• Modulo operation
• Tau (mathematics)