`On Angles and Angular Quantities' Torrens' Reply to Thor's Comments

Torrens, A. B.

doi:10.1088/0026-1394/23/1/008

Cited by 4 publications

(4 citation statements)

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“…"The CIPM decides to interpret the class of supplementary units in the International System as a class of dimensionless derived units for which the CGPM allows the freedom of using or not using them in expressions for SI derived units." (CIPM 1980) and "The coherent unit for any dimensionless quantity is the number one (1). When the value of such a quantity is expressed the unit 1 is generally not written out explicitly.…”

Section: Discussionmentioning

confidence: 99%

On Angles and Angular Quantities

Thor

1987

Metrologia

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Section: Discussionmentioning

confidence: 99%

On Angles and Angular Quantities

Thor

1987

Metrologia

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“…Evidently, the idea of adopting angle as a base quantity was, at that time, quite controversial-as indicated in a subsequent Letter to the Editor of Metrologia by Thor [36] commenting on Torrens's paper, that ends with the admonition: 'Hence it is today out of the question to give a dimension of its own to the quantity plane angle in the SI'. Torrens's reply [37] is a strong rebuttal to Thor's opinion. In the original paper, Torrens again distinguishes between 'geometrical' and 'analytical' angles, following Romain.…”

Section: Review Of Previous Considerations Of Angle As a Base Quantitymentioning

confidence: 97%

Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)

Leonard

2021

Metrologia

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Because of continued confusion caused by the SI's interpretation of angle and solid angle as dimensionless quantities (and the radian and steradian as dimensionless derived units), it is time for the SI to treat these dimensional physical quantities correctly. Building on previous authors' foundations, starting from Euclid's Elements, I argue that angle should be recognized as a base quantity with an independent dimension: angle, A. A dimensionally consistent analysis of rotational geometry and mechanics results in the appearance of a constant of Nature equal to the central angle of a plane circular sector whose arc length is equal to that of its radius. This is the common (but not current SI) concept of the radian, rad, appropriately chosen as the base unit for angle. What the SI calls 'angle' is actually a nondimensionalized angle: the physical angle (dimension A) divided by one radian. Using a coordinate-system-independent definition of solid angle, I show that this is a derived quantity with dimension A 2 and appropriate unit radian-squared. The steradian is retained as a coherent derived unit: sr = rad 2 . Clarification of terminology is needed in distinguishing between 'geometrical' and 'mathematical' trigonometric functions and in related topics, including the distinction between frequency and angular velocity, and between phase and phase angle, among other things.

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“…The symbol x is the same as used in trigonometry [21], where x stands for the 'arc-radius ratio'. The symbol y is used for its associations with 'gonia', the Greek word for angle.…”

Section: Introductionmentioning

confidence: 99%

“…The symbol e in this expression represents the density of mass. The moment of inertia for a cylinder or a disc turning around its axis can be expressed as One important fact should be pointed out: The course of gyration in square c2 can under certain conditions replace the traditional r2 [see, e.g., (18) or (21)]. c2 can, however, never take the place of r2 if r2 is used as measure of the area A [as in ( 2 ) ] .…”

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A New Approach to the Plane Angle

Wittmann¹

1988

Metrologia

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In distinguishing between `category of quantities' and `dimension' the author intends to reach a new understanding of the quantity plane angle. One basis is tensor algebra. Accordingly, the common angle φ (or θ) can be separated into the quantity `arc-radius ratio x' on the one hand and the quantity `angle γ' on the other, each belonging to different categories of quantities.Another basis is the mathematical concept of `embedding'. It allows the mapping of specific `categories of quantities' into a selected `dimension'. Therefore, the category of angles can be embedded either into the `dimension(-less) ratio' or into a specific `dimension angle'.The examples in this paper show that there is no need for a change in teaching mathematics if the angle is explicitly used in defining rotary-motion quantities.The author emphasizes transparency and perspicuity. He argues for an explicit use of the angle γ in rotational mechanics. Furthermore, he suggests that there should be an internationally applicable unit name (e.g. Ri, Re or Ro) for the reference magnitude `full angle Γ'.

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`On Angles and Angular Quantities' Torrens' Reply to Thor's Comments

Cited by 4 publications

References 1 publication

On Angles and Angular Quantities

On Angles and Angular Quantities

Proposal for the dimensionally consistent treatment of angle and solid angle by the International System of Units (SI)

A New Approach to the Plane Angle

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