Dimensional analysis is a simple, physically transparent and intuitive method for obtaining approximate solutions to physics problems, especially in mechanics. It may—indeed sometimes should—precede or even supplant mathematical analysis. And yet dimensional analysis usually is given short shrift in physics textbooks, presented mostly as a diagnostic tool for finding errors in solutions rather than in finding solutions in the first place. Dimensional analysis is especially well suited to estimating the magnitude of errors associated with the inevitable simplifying assumptions in physics problems. For example, dimensional arguments quickly yield estimates for the errors in the simple expression for the descent time of a body dropped from a height h on a spherical, rotating planet with an atmosphere as a consequence of ignoring the variation of the acceleration due to gravity g with height, rotation, relativity, and atmospheric drag.
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MATHEMATICAL TECHNIQUES AND MODELS| April 01 2004
Dimensional analysis, falling bodies, and the fine art of not solving differential equations
Craig F. Bohren; Dimensional analysis, falling bodies, and the fine art of not solving differential equations. Am. J. Phys. 1 April 2004; 72 (4): 534–537. https://doi.org/10.1119/1.1574042
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