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Fundamental Units of Measurement

by Ron Kurtus (27 March 2007)

There are certain units of measurement that are considered fundamental in that they cannot be described as a function of other units. Distance, time and mass are the fundamental units.

Questions you may have include:

• What is distance?
• What are the units of time?
• How is mass defined?

This lesson will answer those questions. There is a mini-quiz near the end of the lesson.

Useful tools: Metric-English Conversion | Scientific Calculator.

Note: If you want to hear the text being read, click the Play button. It takes a few seconds for the sound to start. The voices are somewhat mechanical for computer use.

Time = 4 min. 02 sec.

Distance or length

Distance or length is a fundamental unit of measurement. It is one of three dimensions in space. The only way distance can be measured is to establish some arbitrary length and assign it a value of 1 unit.

Distance is usually denoted by the symbol d.

The meter is the unit of length in the metric system. A kilometer is simply 1000 meters. In the English system the inch is usually considered the unit of length, because larger units such as the foot or yard are made up of inches.

Area is length times width, with the units of square meters, square inches or such.

Volume is length times width times height, the the units of cubic meters, cubic inches or such.

Time

Time is is a fundamental unit of measurement. It is often considered the fourth dimension in the space-time continuum. The only way time can be measured is to use some regular periodic motion and define one period the value of 1 unit.

Time is often denoted as the symbol t.

But note that the measurement of time is dependent on distance, since motion is the change in position over a period of time. Still, it is not a function of distance.

Various units

For example, The rotation of the Earth around the Sun is defined as 1 year, one revolution of the Earth on its axis is defined as 1 day, and one cycle of a pendulum of a certain length defines 1 second.

There are 60 seconds in a minute, 60 minutes in an hour and 24 hours in a day.

Unfortunately, a revolution of the Earth on its axis is not exactly 24 hours. Also, the relationship between a year and a day are not very exact, since about 365.25 days equals one year.

Speed and acceleration

From fundamental units time and distance, we can define other measurements.

Speed is distance divided by time. Velocity is speed that is a specific direction and is usually denoted by the symbol v. Thus, v = d/t.

Acceleration is velocity divided by time. The equation is a = v/t. that cam also be written as a = d/t².

Mass

Mass is is a fundamental unit of measurement. We aren't sure what it is, but we know it is "stuff" that takes up space and has a volume. That means that mass is also somewhat dependent on distance. But it is not a function of distance.

A unit of mass is established by taking an arbitrary amount of a material and defining it as 1 unit. The unit of mass in the metric system is 1 gram. In the English system, the effect of gravity on a unit of mass is measured, such that 1 pound is the unit of weight in that system.

Mass is usually denoted by the symbol m.

Momentum and energy

With the fundamental units of distance, time and mass, we can define momentum as mass times velocity. Momentum is usually denoted by the symbol p, so p = m*v or p = mv.

Energy (E) is 1/2 of mass times velocity times velocity or E = ½mv².

Summary

Units of measurement that are considered fundamental, such that they cannot be described as a function of other units, are distance, time and mass. It can be seen that other measurements are derived from these fundamental units.

Answers to Readers' Questions

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Mini-quiz to check your understanding

1. How was the length of a foot originally determined?

2. What periodic motion does an electric clock use to determine time?

3. Why isn't momentum a fundamental unit?

If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again.

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Fundamental Units of Measurement