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.