Units and Measurement: Dimensions

Dimensions and Dimensional Analysis

"The dimensions of a physical quantity are the powers to which the base quantities are raised to represent that quantity"

Example: Force = mass x acceleration = mass x velocity / time = mass x displacement / time x time = mass x length / time²

Thus, force has one dimension in mass, one in length and minus two in time

Similarly, Density = mass / volume = mass / length³ = mass x length^-3

Thus, density has one dimension in mass and minus three in length.

Thus, all physical quantities can be expressed in terms of fundamental quantities.  But for convenience, the fundamental quantities, instead of writing as such, are represented as follows:

Mass by M, length by L, time by T while electric current, temperature, the amount of substance and luminous intensity are denoted by the symbols of their units, A, K, mol and cd.

Thus, all physical quantities can be expressed in terms of M, L, T, A, K, mol, cd.

In mechanics, all physical quantities can be expressed in terms of only three fundamental quantities - M, L and T

Density = mass / length³ = ML^-3

Force = mass x acceleration = mass x length / time² = MLT^-2

ML^-3 and  MLT^-2 are called dimensional formulae of density and force.