2 Units and dimensions
Table 1.
Quantity Unit Unit abbreviation
Mass kilogram kg
Length metre m
Time second s
Electric current ampere A
Thermodynamic temperature kelvin K
Luminous intensity candela cd
Amount of substance mole mol
Plane angle radian rad
Solid angle steradian sr
kelvin (K):candela (cd):mole (mol):radian (rad):steradian (sr):infinitely long parallel conductors of negligible cross-sectional
area separated by a distance of 1 m in a vacuum, produces a
mutual force between them of 2 x 10 -7 N per metre length
the fraction 1/273.16 of the thermodynamic temperature of
the triple point of water
the luminous intensity, in the perpendicular direction, of a
surface of area 1//600 000 m: of a black body at the tem-
perature of freezing platinum under a pressure of 101 325 Pa
the amount of substance of a system which contains as many
specified elementary particles (i.e. electrons, atoms, etc.) as
there are atoms in 0.012 kg of carbon-
the plane angle between two radii of a circle which cut off on
the circumference an arc equal to the radius
that solid angle which, having its vertex at the centre of a
sphere, cuts off an area of the surface of the sphere equal to
that of a square with sides equal to the radius.
The ~cale temperature (degree Celsius) is the thermodynamic temperature
minus 273.16, so that 0 ~ corresponds to 273.16 K and 0 K corresponds to
-273.16 ~ Note that we write 0 K and 273 K, not 0 ~ nor 273 ~
As an example of how the other units may be derived from the basic units,
velocity is length divided by time. It is usual to write these dimensional
equations using square brackets, with the basic quantities being in capital
letters and the derived quantities being in lower case letters. Thus for this
example we can write [v] - [L]/[T], or
[v] = [L T -1] (1.1)Example 1.
Obtain the dimensions of (1) acceleration, (2) force, (3) torque.Solution
1 Acceleration is the rate of change of velocity, so is velocity/time. Thus