16 Chapter 1. What the ancients knew[[Student version, December 8, 2002]]
Once people used the size of the king’s foot. This book will instead use primarily the Syst`eme
International, orSI units.Inthis system, lengths are measured in meters, masses in kilograms,
time in seconds, and electric charge in coulombs. To clarify the distinction between dimensions and
units, here are some examples:
1.Length has dimensions ofL,bydefinition. In SI units we measure it in meters, abbreviated
in this book asm.
2.Mass has dimensions ofM,bydefinition. In SI units we measure it in kilograms, abbreviated
askg.
3.Time has dimensions ofT,bydefinition. In SI units we measure it in seconds, abbreviated as
s.
4.Velocity has dimensions ofLT−^1 .InSIunits we measure it inms−^1 (pronounced “meters per
second”).
5.Acceleration has dimensions ofLT−^2 .InSIunits we measure it inms−^2.
6.Force has dimensions ofMLT−^2 .InSIunits we measure it inkg m s−^2 ,which we also call
newtonsand abbreviate asN.
7.Energy has dimensions ofML^2 T−^2 .InSIunits we measure it inkg m^2 s−^2 ,which we also call
joulesand abbreviate asJ.
8.Electrical charge has dimensions ofQ,bydefinition. In SI units we measure it in units of
coulombs, abbreviated in this book ascoulto avoid confusion with the symbolC.Theflow
rateof charge, orelectric current,then must have dimensions ofQT−^1 .InSIunits we measure
it in units of coulombs per second, orcoul s−^1 ,also calledamperes,abbreviated asA.
9.(We defer a full discussion of temperature units to Section 6.3.2.)Notice that in this bookall units are set in a special typeface,tohelp you distinguish them from
named quantities (such asmfor the mass of an object).
Wealso create related units by attaching prefixes giga (=10^9 ,orbillion), mega (=10^6 ,ormillion),
kilo (=10^3 ,orthousand), milli (=10−^3 ,orthousandth), micro (=10−^6 ,ormillionth), nano (=10−^9 ,
or billionth), pico (=10−^12 ). In writing, we abbreviate these prefixes toG, M, K, m,μ,n,andp,
respectively. Thus 1Gyis a billion years, 1pNis a piconewton, and so on. Forces in cells are
usually in thepNrange.
Afew non-SI units, likecmandkcal,are so traditional that we’ll occasionally use them as
well. You will constantly find these units in the research literature, so you might as well get good
at interconverting them now. See Appendix A for a list of all the units in this book; Appendix B
presents the hierarchy of length, time, and energy scales of interest to cell biology, and pulls together
the numerical values of many useful constants.
In any quantitative problem, it is absolutely crucial to keep units in mind at all times. Students
sometimes don’t take dimensional analysis too seriously since it seems trivial, but it’s a very powerful
method for catching algebraic errors.Much more importantly,it gives a way to organize and classify
numbers and situations, and even to guess new physical laws, as we’ll see below. Working scientists
eventually realize that when faced with an unfamiliar situation, dimensional analysis is always step
one.
Most constants of Nature have dimensions. Only a few aredimensionlessquantities (also called
“pure numbers”). For example, a geometric angle is dimensionless; it expresses the circumference of