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The first table lists the fundamental quantities used in the International System of Units to define the physical dimension of physical quantities for dimensional analysis. The second table lists the derived physical quantities. Derived quantities can be expressed in terms of the base quantities.
Even when two physical quantities have identical dimensions, it may nevertheless be meaningless to compare or add them. For example, although torque and energy share the dimension T −2 L 2 M, they are fundamentally different physical quantities. To compare, add, or subtract quantities with the same dimensions but expressed in different units ...
The notion of dimension of a physical quantity was introduced by Joseph Fourier in 1822. [2] By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension.
The definitions of the base units have been modified several times since the Metre Convention in 1875, and new additions of base units have occurred. Since the redefinition of the metre in 1960, the kilogram had been the only base unit still defined directly in terms of a physical artefact, rather than a property of nature.
Some physicists have not recognized temperature as a base dimension since it simply expresses the energy per particle per degree of freedom which can be expressed in terms of energy (or mass, length, and time). [4] Duff argues that only dimensionless values have physical meaning and all dimensional units are human constructs. [5]
Dimensionless quantities, or quantities of dimension one, [1] are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. [ 2 ] [ 3 ] Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units .
Examples of non-physical categories are: currency, quality indicator, and colour intensity. Quantities may be grouped together into categories of quantities which are mutually comparable. Lengths, diameters, distances, heights, wavelengths, and so on would constitute such a category. Mutually comparable quantities have the same dimensionality.
James Clerk Maxwell played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.. A coherent system of units is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same ...