Abstract
To introduce the idea of measuring physical quantities, we need concepts like units, dimensions, and characteristic scales. This chapter briefly introduces the reader to these concepts by means of a few examples referring to traffic of cars on motorways, droplets rolling on surfaces, and to the voice of the dragon. Key working tools are dimension renormalization, nondimensionalization, and scaling.
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Notes
- 1.
One can also measure by an inherent scale, or by an external scale if one wants to compare with other experiments.
- 2.
By “scale of units” we mean a complete set of units, representing an a priori given physical situation.
- 3.
The letters “MKS” denote, respectively, “meter”, “kilogram” and “second”. This system is mostly used in electrical engineering.
- 4.
The letters “CGS” denote, respectively, “centimeter”, “gram” and “second”.
- 5.
More such examples having interval scales can be found in sociophysics, econophysics, psychology, economics, etc.; see e.g. [Luc64] and references cited therein.
- 6.
The authors of [G75] and [Paw71] speak about Primär-und Sekundärmaßeinheiten as well as about kohärente Maßeinheiten and das Invarianzprinzip für Abbildungen.
- 7.
often arising as a direct consequence of our tendency to generalize things ...
- 8.
Such a rescaling (or renormalization) is an operation at the level of dimensions; see e.g. [Paw71].
- 9.
This experiment can be easily performed even in big classrooms; just make sure that the tube is sufficiently flexible.
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Muntean, A. (2015). Scaling and Estimation of Physical Systems. In: Continuum Modeling. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-22132-8_1
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DOI: https://doi.org/10.1007/978-3-319-22132-8_1
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