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Dimensional analysis: Difference between revisions

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A dimensional equation can have the dimensions reduced or eliminated through [[nondimensionalization]], which begins with dimensional analysis, and involves scaling quantities by [[characteristic units]] of a system or [[natural units]] of nature. This may give insight into the fundamental properties of the system, as illustrated in the examples below.
 
The dimension of a [[physical quantity]] can be expressed as a product of the base physical dimensions such as length, mass and time, each raised to an integer (and occasionally [[rational number|rational]]) [[power (mathematics)|power]]. The ''dimension'' of a physical quantity is more fundamental than some ''scale'' or [[units of measurement|unit]] used to express the amount of that physical quantity.<ref>{{cite journal |title=A Logico-Linguistic Inquiry into the Foundations of Physics: Part I|journal=Axiomathes |issue=first |doi=10.1007/s10516-021-09593-0|arxiv=2110.03514|last1=Majhi |first1=Abhishek |year=2022 |volume=32 |pages=153–198 |s2cid=238419498 }}</ref> For example, ''mass'' is a dimension, while the kilogram is a particular reference quantity chosen to express a quantity of mass. The choice of unit is arbitrary, and its choice is often based on historical precedent. [[Natural units]], being based on only universal constants, may be thought of as being "less arbitrary".
 
There are many possible choices of base physical dimensions. The [[International System of Units|SI standard]] selects the following dimensions and corresponding '''dimension symbols''':{{anchor|Dimension symbol}}