EXAMPLE 1 In the ISQ, the quantity dimension of force is denoted by dim F = LMT–2.
EXAMPLE 2 In the same system of quantities, dim ρB = ML–3 is the quantity dimension of mass concentration of component B, and ML–3 is also the quantity dimension of mass density, ρ (volumic mass).
EXAMPLE 3 The period T of a pendulum of length l at a place with the local acceleration of free fall g is
Hence dim C(g) = L–1/2 T.
NOTE 1 A power of a factor is the factor raised to an exponent. Each factor is the dimension of a base quantity.
NOTE 2 The conventional symbolic representation of the dimension of a base quantity is a single upper case letter in roman (upright) sans-serif type. The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity Q is denoted by dim Q.
NOTE 3 In deriving the dimension of a quantity, no account is taken of its scalar, vector, or tensor character.
NOTE 4 In a given system of quantities,
- quantities of the same kind have the same quantity dimension,
- quantities of different quantity dimensions are always of different kinds, and
- quantities having the same quantity dimension are not necessarily of the same kind.
NOTE 5 Symbols representing the dimensions of the base quantities in the ISQ are:
Symbol for dimension
amount of substance
Thus, the dimension of a quantity Q is denoted by dim Q = LαMβTγIδΘεNζJη where the exponents, named dimensional exponents, are positive, negative, or zero.