SI Units

This page is about SI Units. This page is created by Jinyoung Lee.

The Main Idea

SI unit stands for the 'International System of Units'. It is the modern form of the metric system, and is the most widely used system of measurement. It is made up of 7 standard units. It justify twenty-two named units, and includes many more unnamed coherent derived units. The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units.

A Mathematical Model

There are some mathematical operation required to translate a non-SI unit to SI unit. For example [math]\displaystyle{ {\frac{lb}{2.2}} = kg }[/math] Since 1 kg(SI unit) is equal to 2.2 lb, to change lb to SI unit, lb has to be divided by 2.2.

Another example can be length. [math]\displaystyle{ {\frac{inch}{0.394}} = cm }[/math] Same method used to change lb to kg. Since 1cm is equal to 0.394inch, inch has to be divided by 0.394 to become SI unit, cm.

Base SI units

This image above shows the base SI units. These units include length, mass, time, electric current, temperature, substance amount, and light intensity.

Prefix

Mass, length or any numbers in physics can be very small or very large. Electron can be a great example. Mass of electron is 0.0000000000000000000000910938356g or 9.10938356 E-31. In SI, prefixes are available to adjust the size of a unit so as to keep the number of those units reasonable. It is kind of difficult to read that number in word. However with the prefix it can be. Image below shows the list of prefixes.

Derived SI units

This image above shows the relationships between many units used in physics based on base SI units. As we can see, most of the units in physics is related to the SI units. It is because there are many quantities that cannot be expressed by a single base SI unit. For example, when talking about the density. it is volume/mass. Mass has it's own SI unit gram. However volumes doesn't. Volume is expressed with derived SI unit, meter cube. As a result, unit for density is [math]\displaystyle{ \mathrm{m}^3/\mathrm{g} }[/math] . Those units are called derived SI units. Units can be combined to create new unit. Some frequently-used combinations have their units named. Here are some examples:

Watt (W), the unit of power.
- [math]\displaystyle{ \mathrm{W} = \mathrm{J}/\mathrm{s} \ }[/math]

Pascal (Pa), the unit of pressure.
- [math]\displaystyle{ \mathrm{Pa} = \mathrm{N}/\mathrm{m}^2 \ }[/math]

Hertz (Hz), the unit of frequency.
- [math]\displaystyle{ \mathrm{Hz} = 1/\mathrm{s} = \mathrm{s}^{-1} \ }[/math]

Newton (N), the unit of force.
- [math]\displaystyle{ \mathrm{N} = \mathrm{kg} \cdot \mathrm{m}/\mathrm{s}^2 }[/math]

Joule (J), the unit of energy.
- [math]\displaystyle{ \mathrm{J} = \mathrm{N} \cdot \mathrm{m} = \mathrm{kg} \cdot \mathrm{m}^2/\mathrm{s}^2 }[/math]

Coulomb (C), the unit of electric charge.
- [math]\displaystyle{ \mathrm{C} = \mathrm{A} \cdot \mathrm{s} }[/math]

Volt (V), the unit of electric potential or voltage.
- [math]\displaystyle{ \mathrm{V} = \mathrm{J}/\mathrm{C} = \mathrm{W}/\mathrm{A} \ }[/math]

Connectedness

This topic can be applied to every aspect of science. When solving the problem, or even when doing a research, every equations and theories are based on SI units. It is a promises between scientists to use the certain unit to reduce the errors or misunderstanding. Therefore, it is very important to know the concept of SI units. This topic is connected to not only physics but also every other scientific subjects. In addition, it might not be familiar in United States, but in the most of the countries they use SI units in ordinary life.

History

The creation of the decimal Metric System at the time of the French Revolution and the subsequent deposition of two platinum standards representing the meter and the kilogram, on 22 June 1799, in the Archives de la Republic in Paris can be seen as the first step in the development of the present International System of Units. In 1832, Gauss strongly promoted the application of this Metric System, together with the second defined in astronomy, as a coherent system of units for the physical sciences. Gauss was the first to make absolute measurements of the earth’s magnetic force in terms of a decimal system based on the three mechanical units millimeter, gram and second for, respectively, the quantities length, mass and time. In later years, Gauss and Weber extended these measurements to include electrical phenomena

References

http://physics.nist.gov/ National institute of standards and Technology.

http://wps.prenhall.com/wps/media/objects/165/169061/blb9ch0104.html Pearson educational site.

Matter & Interactions, Vol. I: Modern Mechanics, 4nd Edition by R. Chabay & B. Sherwood (John Wiley & Sons 2015)

Tutorial & Drill Problems for General Chemistry (and Intro) By Walter S. Hamilton, Ph.D.