Dimensions, Units, Conversion Factors, and Significant Digits (2024)

Relationship

Newton’s second law, F = m a. [Note: Bold notation indicates a vector.] By definition of the fundamental units, this yields 1 lbf = 1 slug× ft/s², or 1 lbf = 32.174 lbm× ft/s².

Conversion

or or

Discussion

The above expressions are dimensionless and each has a value of 1. Thus any of them can be considered a conversion factor with which to multiply or divide any equation to simplify the units.

Example

How much force (in lbf) is required to accelerate a mass of 13.3 lbm at a constant acceleration of 1.20 ft/s²?

Solution:

to the right, since F_x is the x-component of vector F, and a_x is the x-component of acceleration vector a.

Terminology

It is not proper to say that one lbm equals one lbf, but it is proper to say that one lbm weighs one lbf under standard earth gravity. This is obtained by utilizing Newton’s second law with gravitational acceleration, i.e.
.