2.3 CGS Systems of Units
In some fields of physics (e.g. solid-state physics, plasma physics, and astrophysics), it has been customary to
use CGS units rather than SI units, so you may encounter them occasionally. There are several different CGS
systems in use:electrostatic,electromagnetic,Gaussian, andHeaviside-Lorentzunits. These systems differ
in how they define their electric and magnetic units. Unlike SI units, none of these CGS systems defines a
base electrical unit, so electric and magnetic units are all derived units. The most common of these CGS
systems is Gaussian units, which are summarized in Appendix I.
SI prefixes are used with CGS units in the same way they’re used with SI units.
2.4 British Engineering Units
Another system of units that is common in some fields of engineering isBritish engineering units. In this
system, the base unit of length is the foot (ft), and the base unit of time is the second (s). There is no base
unit of mass; instead, one uses a base unit of force called thepound-force(lbf). Mass in British engineering
units is measured units ofslugs, where 1 slug has a weight of 32.17404855 lbf.
A related unit of mass (not part of the British engineering system) is called the pound-mass (lbm). At
the surface of the Earth, a mass of 1 lbm has a weight of 1 lbf, so sometimes the two are loosely used
interchangeably and called thepound(lb), as we do every day when we speak of weights in pounds.
SI prefixes are not used in the British engineering system.
2.5 Units as an Error-Checking Technique
Checking units can be used as an important error-checking technique calleddimensional analysis. If you
derive an equation and find that the units don’t work out properly, then you can be certain you made a
mistake somewhere. If the units are correct, it doesn’t necessarily mean your derivation is correct (since you
could be off by a factor of 2, for example), but it does give you some confidence that you at least haven’t
made a units error. So checking units doesn’t tell you for certain whether or not you’ve made a mistake, but
it does help.
Here are some basic principles to keep in mind when working with units:
- Units on both sides of an equation must match.
- When adding or subtracting two quantities, they must have the same units.
- Quantities that appear in exponents must be dimensionless.
- The argument for functions like sin, cos, tan, sin^1 , cos^1 , tan^1 , log, and exp must be dimensionless.
- When checking units, radians and steradians can be considered dimensionless.
- When checking complicated units, it may be useful to break down all derived units into base units (e.g.
replace newtons with kg m s^2 ).
Sometimes it’s not clear whether or not the units match on both sides of the equation, for example when
both sides involve derived SI units. In that case, it may be useful to break all the derived units down in terms
of base SI units (m, kg, s, A, K, mol, cd). Table H-2 in Appendix H shows each of the derived SI units broken
down in terms of base SI units.