1.2

Units

Physics experiments involve the measurement of a variety of quantities, and a great deal of effort goes into making these measurements as accurate and reproducible as possible. The first step toward ensuring accuracy and reproducibility is defining the units in which the measurements are made.
In this text, we emphasize the system of units known as SI units, which stands for the French phrase “Le S ystème I nternational d’Unités.” By international agreement, this system employs the meter (m) as the unit of length, the kilogram (kg) as the unit of mass, and the second (s) as the unit of time. Two other systems of units are also in use, however. The CGS system utilizes the centimeter (cm), the gram (g), and the second for length, mass, and time, respectively, and the BE or British Engineering system (the gravitational version) uses the foot (ft), the slug (sl), and the second. Table 1-1 summarizes the units used for length, mass, and time in the three systems.

Table 1-1 Units of Measurement

|  | System |
| SI | CGS | BE
Length | Meter (m) | Centimeter (cm) | Foot (ft)
Mass | Kilogram (kg) | Gram (g) | Slug (sl)
Time | Second (s) | Second (s) | Second (s)

Originally, the meter was defined in terms of the distance measured along the earth’s surface between the north pole and the equator. Eventually, a more accurate measurement standard was needed, and by international agreement the meter became the distance between two marks on a bar of platinum–iridium alloy (see Figure 1-1) kept at a temperature of 0 °C. Today, to meet further demands for increased accuracy, the meter is defined as the distance that light travels in a vacuum in a time of 1/299 792 458 second. This definition arises because the speed of light is a universal constant that is defined to be 299 792 458 m/s.

Figure 1-1 The standard platinum–iridium meter bar. (Courtesy Bureau International des Poids et Mesures, France)

The definition of a kilogram as a unit of mass has also undergone changes over the years. As Chapter 4 discusses, the mass of an object indicates the tendency of the object to continue in motion with a constant velocity. Originally, the kilogram was expressed in terms of a specific amount of water. Today, one kilogram is defined to be the mass of a standard cylinder of platinum–iridium alloy, like the one in Figure 1-2.

Figure 1-2 The standard platinum–iridium kilogram is kept at the International Bureau of Weights and Measures in Sévres, France. This copy of the standard kilogram is housed at the National Institute of Standards and Technology. (Sissy Riley, Information Services Division/National Inst of Standards and Technology)

As with the units for length and mass, the present definition of the second as a unit of time is different from the original definition. Originally, the second was defined according to the average time for the earth to rotate once about its axis, one day being set equal to 86 400 seconds. The earth’s rotational motion was chosen because it is naturally repetitive, occurring over and over again. Today, we still use a naturally occurring repetitive phenomenon to define the second, but of a very different kind. We use the electromagnetic waves emitted by cesium-133 atoms in an atomic clock like that in Figure 1-3. One second is defined as the time needed for 9 192 631 770 wave cycles to occur.*

Figure 1-3 This atomic clock, the NIST-F1, is considered one of the world’s most accurate clocks. It keeps time with an uncertainty of about one second in twenty million years. (© Geoffrey Wheeler)

The units for length, mass, and time, along with a few other units that will arise later, are regarded as base SI units. The word “base” refers to the fact that these units are used along with various laws to define additional units for other important physical quantities, such as force and energy. The units for such other physical quantities are referred to as derived units, since they are combinations of the base units. Derived units will be introduced from time to time, as they arise naturally along with the related physical laws.
The value of a quantity in terms of base or derived units is sometimes a very large or very small number. In such cases, it is convenient to introduce larger or smaller units that are related to the normal units by multiples of ten. Table 1-2 summarizes the prefixes that are used to denote multiples of ten. For example, 1000 or meters are referred to as 1 kilometer (km), and 0.001 or meter is called 1 millimeter (mm). Similarly, 1000 grams and 0.001 gram are referred to as 1 kilogram (kg) and 1 milligram (mg), respectively. Appendix A contains a discussion of scientific notation and powers of ten, such as and .

Table 1-2 Standard Prefixes Used to Denote Multiples of Ten

Prefix | Symbol | Factor*
tera | T | 1012
giga* | G | 109
mega | M | 106
kilo | k | 103
hecto | h | 102
deka | da | 101
deci | d | 10−1
centi | c | 10−2
milli | m | 10−3
micro | μ | 10−6
nano | n | 10−9
pico | p | 10−12
femto | f | 10−15

a) |  | Appendix A contains a discussion of powers of ten and scientific notation.

b) |  | Pronounced Jig’a.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.