2.5 Game 2302-0350 units and dimensional analysis  (Page 2/10)

Expressions in this format may be more difficult for people to work with than the multiple line format described above. With enough time and practice, I might become almost as proficient inevaluating expressions as shown in Figure 1 as in evaluating expressions in a multiple-line format, but I'm afraid that I would need a lot oftime and a lot of practice to achieve that proficiency.

We must work with what we are given

However, we must work with what we are given so the mathematical expressions in this module (and most of the other modules as well) will mostly bepresented in a single-line format. The good news is that the single-line format can usually be easily translated into a format thatis suitable for evaluation using JavaScript and other programming languages.

What do we mean by units?

Let me try to answer this important question with an example.

If you were to walk from your home to your school and count your steps, you might report that the distance from your home to your school is 2112 steps or paces. Ifyou are a male student, this would probably be approximately one mile, using assumptions that I will explain later. If you are a female, it would probably besomewhat less than a mile because your pace would probably be a little shorter than your male friend's pace.

A pace is a unit of measurement

In this case, the pace would be a unit of measurement. However, it would not be a standard unit because the length of a pace for one student is often different from the length of a pace for a different student. A male student, forexample, typically has a longer pace length than a female student.

Standard units

Standard units are units whose value has been set by some official agency that has the authority to set standards. One such standard unit is the mile,which as you may know is equal to 5280 foots (more commonly pronounced feet).

A foot (not a feet) is also a standard unit, which you may also know is equal to 12 inches. An inch is another standard unit.

SI units

The discrepancy between the pronunciation of the unit foot and its plural feet is an example of the need for more consistency in the use of units. Many physics books use a system of units called SI units . SI is an abbreviation for a French name, which I am unable to pronounce.

I won't attempt to explain much about SI units. You can probably Google SI units and find hundreds of web pages that explain the system in varying levels of detail.

Tables of SI units

Most of those references will probably also provide tables for the units. I will also attemptto provide tables in Figure 2 and Figure 3 .

Don't ignore the details

Note, however, that you should not ignore the online SI-unit tables altogether. They are likely to contain important information that I won't reproduce here, such as thefact that the meter is a unit of length and its value is the length of the path travelled by light in a vacuum during a time interval of 1/299792458 of a second .