Dimension of Derivative Quantities and Additional Quantities in Physics

Dimension

Dimension of a quantity is a relation between that quantity and base quantities. Dimension of quantities shows how the quantities are arranged upon the base quantities. In physics, there are seven base quantities and that have dimension and two additional quantities that do not have dimension.

However all of derivative quantities have dimension. The dimension of derivative quantities can be found from the dimension of base quantities their derived from.

The dimension of base quantity is stated with capital letter or capital letter in square brackets. To find out, see table below. In that table, there are dimension of base quantity and additional quantities.

Table The Dimension of Base Quantities and Additional Quantities

Base Quantity	Unit	Unit Abbreviation	Dimension
Length	metre	m	[L] = L
Mass	kilogram	kg	[M] = M
Time	second	s	[T] = T
Temperature	kelvin	K	[θ] = θ
Electric current	ampere	A	[I] =I
Luminous intensity	candela	cd	[J] = J
Amount of substance	mole	mol	[N] = N

Additional Quantity	Unit	Unit Abbreviation	Dimension
Plane angle	radian	rad	-
Solid angle	steradian	sr	-

Problem Solving !

 

^@ How to determine the dimension of a unit is as the following ?

1) Velocity dimension

Velocity = displacement / time elapsed

 [v ] = [L] / [T]
 [v ] = [L][T]^-1 =L T^-1

2) Force dimension

Force = mass x acceleration

[F ] = [M][L][T]^-2 = M L T^-2

^@Dimension can be used to prove the similarity of two quantities and two determined the price of derivative quantites.

1) Proving the equivalence between work and quantities of kinetic energy

Work = force x distance

[W ] =  [M][L][T]^-2[L]
          =  [M][L]²[T]^-2

          = M L² T^-2

Kinetic Energy  = ¹/₂ m v²

 [E ] = =  [M][L][T]^-2[L]
          =  [M][L]²[T]^-2
          = M L² T^-2

2) Determining the unit of derivative quantities

Pressure = force / surface area

 P = F / A
[P ] =  [M][L][T]^-2[L]-2
         =  [M][L]^-1[T]^-2
         =  M L^-1 T^-2

Hence, the unit of pressure is kg m^-1 s^-2.