Chapter 4.  Unit Systems

Common US Units

The US system and the British system from which it evolved seem to place a heavy emphasis on the ability to divide numbers evenly by small numbers.  For example, we can divide the number 12 evenly by 2, 3, and 4; the number 16 in half 4 times; and the number 5280 in half six times as well as by 3, 4, 5, and 6.

Common Metric Units

The metric system emphasizes the use of the decimal system of numbers.  Notice that the derivations of related units come from factors of 10.  This makes unit conversions and calculations more convenient, it has become an international standard, especially for scientific publications.  Common conversions from other systems (including the US System) to the metric system can be found at websites such as:

http://www.convertit.com/Go/Bioresearchonline/Measurement/Units.ASP (Conversions)

http://www.chezcrowe.com/conv_app.htm (Conversion)

10^-24 m/ym

10^24 ym/m

Since the metric system is conveniently based on the decimal system, we can use prefixes to create units related to a given unit by factors of ten.  For example, a kilogram (using the prefix "kilo") is a new unit derived from the unit gram by multiplying by 1000.  The above table gives the unit identities that convert between such units.

The metric system begins with a definition of  the unit "meter" for the dimension "length" based on the natural phenomena of the curvature of the earth which a person can determine using trigonometry to a reasonable amount of accuracy anywhere on the earth.  Later scientists gained more accuracy by using natural concepts of light.  The choice of meter came close to the commonly used unit of a yard.

The metric system defines the unit "liter" for the dimension "volume" as a cubic decimeter.  This particular choice of how a liter depends on a meter results in a volume unit close to the unit "quart".  Now using the natural phenomena of water, the metric system defines the unit "kilogram" of the dimension "mass" as the mass of water contained in one liter.  This means that a gram of water fills a cube having one-centimeter edges.

Today, they use the unit joules to measure energy and the relationship between calories and joules for a particular substance (in addition to just water) is the specific heat of that substance. For  more information see http://library.thinkquest.org/C004970/thermo/specific.htm?tqskip1=1

Common SI Units

The seven base units create the foundation from which we derive all other SI units.  Notice that each unit combines previously defined units using simple division and multiplications.  In fact, most of units relate back to the first three base units (meters, kilograms, and seconds) through simple algebraic substitutions.  A 75 watt light bulb refers to a 75 kg*m²/s³ light bulb where we have the chain of derivations: W=J/s=N*m/s= (kg*m/s²)*m/s= kg*m²/s³.  Even the base unit "ampere" relates back to the first three units through the relationship between magnetic forces and electronic currents; briefly, an ampere represents the amount of current in two straight parallel wires set 1 meter apart to produce a magnetic force of 2*10^-7 newtons. (See http://physics.nist.gov/cuu/Units/units.html)

The angle units represent supplementary units that use length and area to measure plane and solid angles respectfully.  You can find more information concerning the SI System of Units at sites such as:

http://metre.info/ (Extensive Details of SI or Modern Metric System)

http://www.metricmethods.com/metricmoments.html

The Unified Math® system of units adds two new base units to the SI system, allowing us to handle business and statistical problems.

Most measuring instruments relate values of a given dimension to the values in other dimensions.  Usually the other dimension is "length" with an associated a scale.  A traditional thermometer relates the expansion of some material (like mercury) in a tube that has been calibrated with a scale that measures the length that the material expands.  Consider modern cars, we relate the dimension "rotation" of the tires to the gauge in a speedometer where a needled moves a particular length and turns a counter for mileage.  Earlier, on some covered wagons, they had a device that counted the dimension "rotation of the wheel".  From that information, they could then calculate the approximate distance traveled.

The process of calibrating a measuring instrument often involves adjusting the size of one dimension to match a predefined value of another dimension.  Take for example a kitchen scale that measures weight based on a spring inside the measuring instrument.  Such a device quite often has a knob (shown on the back of the one above) that allows the user to adjust the pointer connected to the spring so that it lines up with the 0 mark on the scale.

The choice of units determines the form of the equation.  It is not sufficient just to say that distance equals the velocity (speed) times the time.  We need to also specify the units of each quantity in the equation.

 Activities:

Explorations:

Exercises:

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Copyright © 2004  Dr. Ranel E. Erickson