Dimensions and Units

Key Concept: There are four fundamental dimensions in the study of

Engineering Mechanics. They are force, F, mass, M, length, L, and time, T.

Associated with each dimension are appropriate English and metric units.

In a Nut Shell: To form a consistent set of units, one selects the units for three of

the fundamental dimensions, called the primary dimensions. There are two systems,

the FLT system and the MLT system as given in the table below. You may use

either system.

Primary dimensions FLT System	F	L	T
Primary dimensions MLT System	M	L	T

The dimension of mass, M, can be related to the dimension of force, length, and time

using Newton’s Second Law.

F = m a

where F is the force acting on a particle with the dimension F

m is mass of the particle with the dimension M

a is the acceleration of the particle with the dimensions L/T²

So using dimensions and Newton's Law: F = M L/T² and M = FT² / L

which are the dimensions of M in terms of the primary dimensions F, L, and T

Table of Consistent Units for each Dimension

Units	Force	Mass	Length	Time
English	pounds (lb)	slugs*	feet (ft)	Seconds
Metric	newtons*	kilogram (kg)	meters (m)	Seconds

* Denotes derived unit; all others are primary units

Return to Notes on Statics

Copyright © 2019 Richard C. Coddington
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