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The dimensions of a physical quantity are associated with combinations of mass, length, time, electric charge, and temperature, represented by sans-serif symbols M, L, T, Q, and Θ, respectively, each raised to rational powers.
Note that dimension is more abstract than scale unit: mass is a dimension, while kilograms are a scale unit (choice of standard) in the mass dimension.
As examples, the dimension of the physical quantity speed is "distance/time" (L/T or LT −1), and the dimension of the physical quantity force is "mass × acceleration" or "mass×(distance/time)/time" (ML/T2 or MLT −2). In principle, other dimensions of physical quantity could be defined as "fundamental" (such as momentum or energy or electric current) in lieu of some of those shown above. Most physicists do not recognize temperature, Θ, as a fundamental dimension of physical quantity since it essentially expresses the energy per particle per degree of freedom, which can be expressed in terms of energy (or mass, length, and time). Still others do not recognize electric charge, Q, as a separate fundamental dimension of physical quantity, since it has been expressed in terms of mass, length, and time in unit systems such as the electrostatic cgs system. There are also physicists that have cast doubt on the very existence of incompatible fundamental dimensions of physical quantity.[3]
The unit of a physical quantity and its dimension are related, but not precisely identical concepts. The units of a physical quantity are defined by convention and related to some standard; e.g., length may have units of metres, feet, inches, miles or micrometres; but any length always has a dimension of L, independent of what units are arbitrarily chosen to measure it. Two different units of the same physical quantity have conversion factors between them. For example: 1 in = 2.54 cm; then (2.54 cm/in) is called a conversion factor (between two representations expressed in different units of a common quantity) and is itself dimensionless and equal to one. There are no conversion factors between dimensional symbols.
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