On Angles and Angular Quantities

1986/01/01 by Arnau Torrens · 8 citations
Engineering · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry

paper · doi:10.1088/0026-1394/22/1/002

openalex publication_date 1986/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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 φ on a circle of radius R is written as s = η R φ, 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 .

Citations

• A Viewpoint on the Quantity "Plane Angle"

Cited by

• The next 50 years of the SI: a review of the opportunities for the e-Science age
• The range of options for handling plane angle and solid angle within a system of units
• On the dimension of angles and their units
• Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)
• Implications of adopting plane angle as a base quantity in the SI
• On the status of plane and solid angles in the International System of Units (SI)
• Angles in the SI: a detailed proposal for solving the problem
• Radian [wikipedia]