On Angles and Angular Quantities
Abstract
It is argued that angles are geometric quantities and have a dimension. The equation giving the length s of the arc cut out by an angle varphi on a circle of radius R is written as s = η R varphi, where η is a universal constant relating translational and rotational mechanics.
Examples chosen in trigonometry and rotational mechanics show how a few equations can be rewritten so that all equations involve only quantities (including angles), and constants (such as η), and do not require the use of special units, such as the radian. Once angular dimensions have been properly incorporated in quantities and equations, it becomes clear, for example, that an angular frequency or velocity can be expressed in rad/s, or °/s, or rev/min. but not in Hz or s^{1}.
 Publication:

Metrologia
 Pub Date:
 January 1986
 DOI:
 10.1088/00261394/22/1/002
 Bibcode:
 1986Metro..22....1T