Dimensions are defined as quantities that can be measured. Each dimension has units which are arbitrary names that correlate to particular dimensions to make it relative. In Systeme International (S.I.) system of units which is the commonest system used for scientific measurement in the world, seven (7) dimensions correspond to seven (7) fundamental/base quantities that commonly apply to all kinds of quantities in existence. These fundamental quantities and their corresponding dimensions include: mass [M], length [L], time [T], thermodynamic temperature [θ], amount of substance [N], electric current [A], and luminous intensity [CD]. Note that N stands for number of substances, A stands for Ampere, θ stands for kelvin while CD stands for Candela. Quantities are usually presented together with their units but in order to insert correctly the unit to each quantity, the dimensions of the quantity have to be properly defined first from the formula used to determine the quantity.
For instance, the unit of some dimensions such as length is metre (m), mass is kilogram (kg) while temperature is kelvin (K). To determine the dimension of density or mass density, we first recall that density is equal to the ratio of mass to volume (density = mass/volume). The dimension of mass is [M] as shown earlier. A volume is bounded by length in three dimensions. Thus, volume = length x length x length = (length)3. Since the dimension of length is [L], the dimension of volume is [L3]. This implies that the dimension of mass density = [M]/[L3] = [ML-3]. To determine the unit of mass density from the dimension, we recall that the unit of mass is kilogram (kg), and the unit of length is metre (m). Thus, the unit of mass density would be equal to kg/m3 of kgm-3. The table below presents the dimensions and units of common derived quantities in engineering practice.
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