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APPENDIX B Units of Measurement

Scientific and technical calculations often involve numbers that include units of measurement. It is very important to be able to work with these numbers algebraically. Performing operations on numbers with units and converting between units are discussed in Section 1.4. Included in that section are tables of conversion factors and metric prefixes as well as several examples and exercises involving units and unit conversions. This appendix is intended to provide an overview of the types of units used in this book, including the quantities they measure, their symbols, and how some units are derived from others.

There are two basic systems of units, the SI metric system (International System of Units) and the U.S. customary system. The SI metric system (which includes the meter, kilogram, and newton, for example) is used worldwide in all scientific work and in business related to international commerce. Most countries in the world use the SI metric system for all measurements in science, industry, and everyday activities.

The U.S. customary system (which includes the foot, pound, and mile, for example) is the system historically used by the United States. In the 1970s and 1980s, there was a trend in the United States to change to the metric system in order to align itself with most other countries. However, that trend lost its steam in the 1990s, and today, both the metric system and the U.S. customary system are used. For this reason, this book uses both SI and U.S. customary units in the examples and exercises. Technicians and engineers must be able to use both systems and convert units from one system to the other.

In each system, universally accepted base units are used to measure certain fundamental quantities. For example, the base units for length are the foot (U.S.) and the meter (SI). The base unit for time is the second in both systems. There is one case where the base units used in the two systems measure different, but related, fundamental quantities. The U.S. customary system uses the pound as the base unit for force, whereas the SI system uses the kilogram as the base unit for mass. Since force and mass are two different quantities, it is not really proper to convert from one to the other. However, this conversion is frequently done by using the fact that 1 kilogram exerts a force of 2.205 pounds near Earth’s surface (this conversion would not be valid anywhere except near Earth’s surface).

In the SI system, there are seven different base units, which are shown in boldface type in Table B.1 on the next page. Other units are expressed in terms of the base units. For example, the SI unit for force is the newton (N), which is defined by $1 N = 1 \frac{m \cdot kg}{s^{2}} .$ $1 N = 1 \frac{m \cdot kg}{s^{2}} .$ Here, the newton is expressed in terms of the base units meter (m), kilogram (kg), and second (s). Units such as this are called derived units. Not all combinations of base units are given special names. For example, the U.S. customary unit for acceleration is $\frac{ft}{s^{2}}$ $\frac{ft}{s^{2}}$ (without any special name). Table B.1 gives a listing of all the commonly used units, their symbols, and how each of the derived units are expressed in terms of other units.

Table B.1 Quantities and Their Associated Units

		Unit
		U.S. Customary		Metric (SI)
Quantity	Quantity Symbol	Name	Symbol	Name	Symbol	In Terms of Other SI Units
Length	`s`	foot	ft	meter	m
Mass	`m`	slug		kilogram	kg
Force	`F`	pound	lb	newton	N	$m \cdot kg / s^{2}$ $m \cdot kg / s^{2}$
Time	`t`	second	s	second	s
Area	`A`		${ft}^{2}$ ${ft}^{2}$		$m^{2}$ $m^{2}$
Volume	`V`		${ft}^{3}$ ${ft}^{3}$		$m^{3}$ $m^{3}$
Capacity	`V`	gallon	gal	liter	L	$(1 L = {1 dm}^{3})$ $(1 L = {1 dm}^{3})$
Velocity	`v`		ft/s		m/s
Acceleration	`a`		$ft / s^{2}$ $ft / s^{2}$		$m / s^{2}$ $m / s^{2}$
Density	`d`, $ρ$ $ρ$		$lb / {ft}^{3}$ $lb / {ft}^{3}$		$kg / m^{3}$ $kg / m^{3}$
Pressure	`p`		$lb / {ft}^{2}$ $lb / {ft}^{2}$	pascal	Pa	$N / m^{2}$ $N / m^{2}$
Energy, work	E, W		$ft \cdot lb$ $ft \cdot lb$	joule	J	$N \cdot m$ $N \cdot m$
Power	`P`	horsepower	hp	watt	W	J/s
Period	`T`		s		s
Frequency	`f`		1/s	hertz	Hz	1/s
Angle	$θ$ $θ$	radian	rad	radian	rad
Electric current	I, i	ampere	A	ampere	A
Electric charge	`q`	coulomb	C	coulomb	C	$A \cdot s$ $A \cdot s$
Electric potential	V E	volt	V	volt	V	$J / (A \cdot s)$ $J / (A \cdot s)$
Capacitance	`C`	farad	F	farad	F	$s / Ω$ $s / Ω$
Inductance	`L`	henry	H	henry	H	$Ω \cdot s$ $Ω \cdot s$
Resistance	`R`	ohm	$Ω$ $Ω$	ohm	$Ω$ $Ω$	V/A
Thermodynamic temperature	`T`			kelvin	K	(temp. interval $1 ° C = 1 K)$ $1 ° C = 1 K)$
Temperature	`T`	degrees Fahrenheit	$° F$ $° F$	degrees Celsius	$° C$ $° C$
Quantity of heat	`Q`	British thermal unit	Btu	joule	J
Amount of substance	`n`			mole	mol
Luminous intensity	`I`	candlepower	cp	candela	cd

Special Notes:

The SI base units are shown in boldface type.
Other units of time, along with their symbols, that are used in this book are the minute (min), hour (h), and day (d).
This table includes most of the units used in this book. Occasionally, other units will be noted and used.
In addition to the radian, the units degree $(°)$ $(°)$ and revolution (r) are commonly used to measure angles or rotations.
Other common U.S. units that are used in this text are the inch (in.), yard (yd), mile (mi), ounce (oz), quart (qt), ton, and acre.
Unit symbols are case sensitive. They should be written exactly as shown in the table.
The dot symbol is used to show units are multiplied.

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Table of Contents for APPENDIX B Units of Measurement

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Table of Contents for
APPENDIX B Units of Measurement