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Dimensions of plane and solid angles and their units in the International System of Units (SI)
https://doi.org/10.32446/0368-1025it.2020-10-26-32
Abstract
The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.
About the Authors
M. I. Kalinin
Russian Research Institute for Metrological Service (VNIIMS)
Russian Federation
Russian Federation
Mikhail I. Kalinin
Moscow
L. K. Lev K. Isaev
Russian Research Institute for Metrological Service (VNIIMS)
Russian Federation
Russian Federation
Lev K. Isaev
Moscow
F. V. Bulygin
Russian Research Institute for Metrological Service (VNIIMS)
Russian Federation
Russian Federation
Fedor V. Bulygin
Moscow
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Review
For citations:
Kalinin M.I., Lev K. Isaev L.K., Bulygin F.V. Dimensions of plane and solid angles and their units in the International System of Units (SI). Izmeritel`naya Tekhnika. 2020;(10):26-32. (In Russ.) https://doi.org/10.32446/0368-1025it.2020-10-26-32
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