Newton's
second law, F = ma, is ubiquitous in science, technology, and just about
anything that involves the consideration of forces, mass, and accelerations, in
other words, dynamics.

F = ma is also the basis for the definition of units of force, and in
particular, for the relationship between units of force, and units of
mass. There is occasionally some confusion over the relationship between force,
and mass, or more specifically between the units of force and mass. A
particular area of irritation concerns English units of force and mass, and the need
to include 32.2 in the relationship between these two units.

To clear up this situation, I've prepared a little chart that I hope will shed
some light on the important relationship between force, mass and
acceleration. Here's the chart:

In all cases, Force equals mass times acceleration. In each column, a particular unit of force is
presented and what it relates to in terms of mass and the appropriate magnitude
of acceleration. Here, one can see that
the value of 32.2 arises in the relationship between pounds of force and pounds
of mass is because this relationship is defined by a specific value for of
acceleration, which in this case is 32.2 and is, in fact, the acceleration due
to gravity here on Earth. It turns out
that it is very handy to have a unit of force have the same magnitude (*not*
the same units) as a unit of mass when you’re on the surface of the Earth. This is why, perhaps to the surprise of
American engineers, that there is a commonly used measure of force used in Europe known as the kilogram force, and for the exact
same reason.

Another interesting observation is that, if you want to do
away with that pesky 32.2 value when using English units, then simply switch over
to using the poundal, which is simply one pound of mass accelerated at 1
ft/sec^2, completely analogous to the realationship between Newtons and kilograms.

There are other even more obscure units of force and mass, which
are not shown here. As I come across
others, or you readers have suggestions, I will include them in future updates
of this charts.

However, the point of this chart is to simply organize
units of force, mass, and acceleration, based on their origin, which is Newton’s Second Law. I hope that by so doing, it will be easier to
visualize the actual relationships between these units, and make it easier to
keep them straight in your head.