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| Working Group 5.23 |
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Angle Metology
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The physical quantity "plane angle"
Definition, units, realization
In the International System of Units, the unit of plane angle, the
radian (symbol: rad), is classified as an SI derived unit (together with the unit of solid angle, the steradian). The radian is defined as the plane angle which, as the central angle of a circle 1 m in radius, cuts off on the circumference an arc of 1 m.
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From this it follows that the angle can be traced back to two lengths.
With the arc length of the circumference one obtains the so-called round angle 2 π rad as a natural, invariable and error-free angle standard. The realization of the plane angle can, therefore, be derived most exactly from the division of a circle. As the number π is indivisible, the unit of angle rad is, however, unsuitable for practical metrology purposes. Instead, the traditional units
degree (°), minute ('), and second (") are used in the sexagesimal system to subdivide the round angle:
360° = 2 π rad
1° = ( π/180) rad
1' = (1/60)° = ( π/10 800) rad
1'' = (1/60)' = (π/648 000) rad
In addition, the unit of angle gon, also referred to as grade, with the round angle subdivided into 400 parts, is commonly used for measurements in the field of geodesy:
400 gon = 2 π rad
1 gon = (π/200) rad
The gon is subdivided into decimals. The units used are: the centigon or centesimal minute (0,01 gon), the milligon (0,001 gon) and the centesimal second (0,0001 gon).
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