2Dimensional analysis
IA Dynamics and Relativity
2.1 Units
People use units to represent dimensional quantities. A unit is a convenient
standard physical quantity, e.g. a fixed amount of mass. In the SI system, there
are base units corresponding to the basics dimensions. The three we need are
– meter (m) for length
– kilogram (kg) for mass
– second (s) for time
A physical quantity can be expressed as a pure number times a unit with the
correct dimensions, e.g.
G = 6.67 × 10
−11
m
3
kg
−1
s
−2
.
It is important to realize that SI units are chosen arbitrarily for historical reasons
only. The equation of physics must work in any consistent system of units. This
is captured by the fact that physical equations must be dimensionally consistent.