2.8 Dimensions of physical quantities

Dimensions Of Physical Quantities

The nature of a physical quantity is described by its dimensions. All the physical quantities represented by derived units can be expressed in terms of some combination of seven fundamental or base quantities. We shall call these base quantities as the seven dimensions of the physical world, which are denoted with square brackets [ ]. Thus, length has the dimension [L], mass [M], time [T], electric current [A], thermodynamic temperature [K], luminous intensity [cd], and amount of substance [mol]. The dimensions of a physical quantity are the powers (or exponents) to which the base quantities are raised to represent that quantity. Note that using the square brackets [ ] round a quantity means that we are dealing with the dimensions of the quantity.

Example:

Force, as the product of mass and acceleration, can be expressed as
Force = mass \(\times\) acceleration
\(=\) mass \(\times\) (length) \(/(\text { time })^{2}\)
The dimensions of force are \([\mathrm{M}][\mathrm{L}] /[\mathrm{T}]^{2}=\) [M L T \({ }^{-2}\) ]. Thus, the force has one dimension in mass, one dimension in length, and \(-2\) dimensions in time. The dimensions in all other base quantities are zero.