Fundamental Units of Measurement

You measure things in terms of multiples of units.

A fundamental unit of measurement is one that they cannot be described as a function of other units.

Distance, time and mass are the fundamental units.

• measuring in units
• Suppose there are 7 units.
• Other possibilities

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.

Measuring in units

In order to measure something, you need to define a unit of measurement. "Unit" refers to 1. In this way, all measurements are multiples of that unit.

Originally, the English unit foot was the length of the King's foot. Thus, a distance of 25 feet was 25 time the foot unit of measurement.
Unfortunately, each King had a different sized foot, so that brouhgt about some confusion. Finally, they agreed on a standard length for a foot that would not vary.

SI base units

The International System of Units (SI) defines seven units of measure as a basic set from which all other SI units are derived. These SI base units and their physical quantities are:[1]

• metre for length
• kilogram for mass
• second for time
• ampere for electric current
• kelvin for temperature
• candela for luminous intensity
• mole for the amount of substance.

The SI base quantities form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology. However, in a given realization of these units they may well be interdependent, i.e. defined in terms of each other.[1

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 units of cubic meters, cubic inches or such.

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.

Time

Time 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 has 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 can also be written as a = d/t².

Electric current

"The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per metre of length."

Electric current means, depending on the context, a flow of electric charge (a phenomenon) or the rate of flow of electric charge (a quantity).[1] This flowing electric charge is typically carried by moving electrons, in a conductor such as wire; in an electrolyte, it is instead carried by ions, and, in a plasma, by both.[2]

The SI unit for measuring the rate of flow of electric charge is the ampere, which is charge flowing through some surface at the rate of one coulomb per second. Electric current is measured using an ammeter.[1]

Temperature

Luminous intensity

Amount of substance.

Problems or disagreements

Electric current

Since electric current is the movement of electrons in a conducting wire, it appears to require a man-made device. To me, this does not seem to be a good candidate for a base of fundamental unit of measurement.

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.