WEIGHTS & MEASURES

Two systems of weights and measures coexist in the United States today: the U.S. Customary System and the International System of Units (SI, after the initials Systeme International). The SI System, commonly identified with the metric system, is actually a more complete and coherent version of it. Throughout U.S. history, the Customary System (inherited from, but now different from, the British Imperial System) has been generally used.

The use of the SI System has slowly and steadily increased in the United States, particularly in the scientific community; however, the general public still uses, almost exclusively, the U.S. Customary System. Because this Web site has a large international audience, all calculations and example problems make exclusive use of SI units, however the formulae provided will work in either system of units. Whenever a basic constant is given, its U.S. Customary equivalent is also given in parentheses.

In the SI System, the basic units are the units of length, mass, and time, and are called respectively, the meter (m), the kilogram (kg), and the second (s). The unit of force, called the Newton (N), is a derived unit and is defined as the force that gives an acceleration of 1 m/s² to a mass of 1 kg.

In the U.S. Customary System the base units are the units of length, force, and time, and are called respectively, the foot (ft), the pound (lb), and the second (s). The unit of mass, called the slug, is a derived unit and is defined as the mass that receives an acceleration of 1 ft/s² when a force of 1 lb is applied to it.

When working in the U.S. Customary System, it is commonplace to express "mass" in pounds; however, when doing so, it is necessary to recognize that we are actually expressing "weight", which is the measure of the gravitational force on a body. When used in this way, the weight is that of a mass when it is subjected to an acceleration of one g. In the study of dynamics, where forces, masses, and accelerations are involved, it is important that we express the mass m in slugs of a body of which the weight W has been given in pounds. That is, m=W/g, where g is approximately equal to 32.174 ft/s².

It is sometimes common practice for mathematical equations to be expressed in such a way that the variable for mass is entered in the unit of pounds. These equations include a term that converts mass from pounds into its proper unit of slugs. When using these equations, one must proceed with caution because they are only valid when using U.S. Customary units. When using SI units, it is necessary to use a different equation that does not contain the conversion factor. To avoid this problem, all equations used in this Web site require that mass be expressed in the unit of slugs in the U.S. Customary System, and kilograms in the SI System.