About slugs and pound units

 This post is intended to provide a common ground on the usage of these Imperial and US customary units.

The units $slugs$ and pound-mass ($lb_m$) are sometimes used as synonyms for mass units. However, only the $slug$ is a true unit of mass.

The $lb_m$ is something else. The equivalence between these two quantities is,

$1\, slug=1\, lb_f\cdot s^2/ ft= \dfrac{1\,lb_m}{32.17\,ft/s^2}$        Eq. (01)

where the unit $lb_f$, or pound-force, was introduced too. Many times, instead of writting $lb_f$, people just write $lb$. Also, $1.0\, lb_f$ has a mass of $1.0\, lb_m$ and the only way the above Eq. (01) really works is by introducing the constant $g_c$ as follows,

$g_c=\dfrac{32.17\, lb_m}{lb_f/\left( ft/s^2 \right)}=\dfrac{32.17\,lb_m\cdot ft/s^2}{lb_f}$        Eq. (02)

which is as you can see a adjusting parameter to fix the unit system.

One in which this $g_c$ occurs is in the well known formula,

$F=mg$        Eq. (03)

to calculate the force $F$ from the mass $m$ and the acceleration due to gravity $g$. Equation (03) works well in SI units but not if Imperial units are introduced. For these purposes, Eq. (03) must be changed to,

$F=m\dfrac{g}{g_c}$        Eq. (04)

Otherwise, physical inconsistencies would arise. However, another remedy is possible: make use of $slugs$ rather than $lb_m$, so that $g_c$ is no longer needed.

Working with Imperial units can be confusing but using the presented equivalencies you will succeed (hopefully).