On Angles and Angular Quantities

Torrens, A. B.

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

Cited by 21 publications

(31 citation statements)

References 6 publications

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“…The contradictions between the intuitive conception of the angles as dimensional quantities and the mathematical relations accepted for the defining of the angles as dimensionless quantities have led to the appearance of a large number of the papers analyzing this case. Some authors [7,8] proposed to change the relation for the plane angle, introducing into it a dimensional coefficient. In the papers by other authors [8][9][10][11][12], it was proposed to consider the plane angle as dimensional and refer it to the base quantities, and its unit, the radian, to the base SI units.…”

Section: On the Status Of Plane And Solid Angles In The International...mentioning

confidence: 99%

On the status of plane and solid angles in the International System of Units (SI)

Kalinin

2019

Metrologia

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The article analyzes the arguments that became the basis for declaring in 1995, at the 20th General Conference on Weights and Measures that the plane and solid angles are dimensionless derived quantities in the International System of Units. The inconsistency of these arguments is shown. It is found that a plane angle is not a derived quantity in the SI, and its unit, the radian, is not a derived unit. A solid angle is the derived quantity of a plane angle, but not a length. Its unit, the steradian, is a coherent derived unit of the radian.

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Section: On the Status Of Plane And Solid Angles In The International...mentioning

confidence: 99%

On the status of plane and solid angles in the International System of Units (SI)

Kalinin

2019

Metrologia

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“…The anomalous handling of the radian and steradian within the SI, and indeed all other unit systems, whereby plane angle and solid angle have independently defined units, radians and steradians, as if they are base quantities, but are also treated as if they are dimensionless (with the unit 'm m −1 ' or 'm 2 m −2 ' respectively), has been widely discussed elsewhere (e.g. Brinsmade 1936, Torrens 1986, Brownstein 1997, Mohr and Phillips 2014, Quincey and Brown 2016, Quincey 2016. Between 1960 and 1995 the radian and steradian belonged to a specially created category of 'supplementary units'.…”

Section: The Example Of Angle Unitsmentioning

confidence: 99%

“…We use the symbol η for this constant, as given inTorrens (1986) and elsewhere Brownstein (1997). used the symbol □;Brinsmade (1936) and several others did not use a special symbol, but adopted the unit symbol 'rad' for use as a constant, so that η = 1/rad.…”

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confidence: 99%

A clearer approach for defining unit systems

Quincey¹,

Brown²

2017

Metrologia

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We present the SI and other unit systems, including cgs-em and cgs-es, in a framework whereby a system of fully independent and dimensionally orthogonal base units is modified by conventions designed to simplify the equations that are used within each system. We propose that the radian can be seen as an independent unit whose dimensional status is modified in the SI and other unit systems for this purpose.This framework clarifies how different unit systems are interrelated, and identifies the key pieces of information that are needed to define both a unit system and the equations that are to be used with it. Specifically, these are the size of the base units in the unsimplified system, together with sufficient equations to identify all the conventions adopted by the particular unit system. The appropriate extra information for the revised SI is presented. We do not propose that the treatment of angles as dimensionless within the SI is changed.It is also proposed that the Gaussian unit system is best seen as identical to cgs-es, but with the B and H symbols in equations used to represent "relativistic" versions of B and H, which should properly be treated as different quantities. These different versions of B and H can similarly be used within the SI, with many of the advantages of the Heaviside-Lorentz system.

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“…The subject of the identity of measurands-a central topic for chemical measurement-is unmentioned. There are well-documented problems, confusions and inconsistencies in the treatment of angular measures and rotationssome of the oldest and most basic measurements known to our species [30][31][32][33][34]. All of these are creating large difficulties for modern technologies.…”

Section: Some Disquiet Concerning the New Simentioning

confidence: 99%

No prospect for change

Price¹

2011

Accred Qual Assur

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A recent discussion by Martin Milton in the November issue of this journal was critical of many published objections to the proposed new International System (SI) measurement units (and in particular the definition of the mole) on the grounds that many objectors had proposed new terms in attempts to clarify thinking and that it is impractical to achieve consensus on such proposals. This discussion in response argues that those criticisms miss the point of the objectors' arguments and are perhaps more appropriately directed at both the current and the new SI itself. A primary example of a neologism in the SI is the term ''amount of substance.'' The many substantive problems with the new SI remain unaddressed by its proponents. Many important consequences of exactly fixing multiple inter-dependent fundamental physical constants as the basis of the world's measurements would appear not to have been considered by the global institutions responsible for the world's measurement units.

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On Angles and Angular Quantities

Cited by 21 publications

References 6 publications

On the status of plane and solid angles in the International System of Units (SI)

On the status of plane and solid angles in the International System of Units (SI)

A clearer approach for defining unit systems

No prospect for change

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