Article Review: Mohr et al 1206z (2022d)
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Title: Article Review: Mohr et al 1206z (2022d) Reviewer: John Volan Review Date: 120Az (2026d) Reviewed Article: On the dimension of angles and their units, Peter J. Mohr & Eric Shirley (National Institute of Standards and Tecnology), William D. Phillips (Joint Quantum Institute), Michael Trott (Wolfram Inc.), 11BB-05-24z (2015-05-28d) Subject: Angular mechanics and other units in SI (and Primel) This article review was adapted from a series of posts in the Article Reviews about Angular Units thread on the DozensOnline at tapatalk, and continues the discussion begun in Article Review: Mohr & Phillips 11BBz (2015d) The reviewed article goes into more depth on the implications of granting angular quantities true dimension, as opposed to the dimensionless interpretation under SI. It revisits the notion of “complete” versions of trigonometric and other transcendental functions, and examines how those interact with calculus. It resolves dimensional dilemmas in such operations by showing how a differential with respect to angle can result in a constant of angular dimension being extracted, with a value that turns out to be a radian, which allows the dimensional analysis to balance. The article then applies this calculus technique to various physical applications involving angular quantities and their related transcendental functions, resolving dimensional imbalances caused by SI’s approach. The article review strengthens the argument by using the diacritical notations introduced in the previous article review to clarify the symbols and formulas. It also expresses the examples using Primel units to more clearly show the dimensionalities of the quantities via Primel’s “Quantitel” style unit names. |
