Weight vs. Mass

It is funny every since I've been working with kinetic physics since around 2007, I finally now figured out the difference between weight and mass. This on the surface seems like a no-brainer, but it gets a bit murky when dealing with Kilograms and Pounds. So let me share with you my spin on these terms, which are presented in such a way to help avoid confusion when dealing with physics equations.

Let me start off by saying that weight is a measurement of force, where mass is a component of force. Since weight is a force this would imply that a scale would also be a measurement of force. Let's define scale... I don't care for the digital ones or the fancy ones that use the counter-weight. Instead, I like the small portable analog ones that use spring tension (you'll see why in a moment). So using the scale and I stand on it and look at the numbers it says I weigh 150 pounds. The pounds here are presented as pound-force or as I like to put it, "Pound as force using gravity". When we use the term pound we generally refer to pound-force.

So we can observe weight or force in this regard and force is mass times acceleration (f=ma). Ok to further define force, acceleration is a measurement in the change of velocity, and velocity is speed with a direction, where speed is a measurement of displacement of an object given an amount of time. So then back to the weight definition you may say, well James, you are not moving when you stand on the scale; therefore your speed is 0 and therefore your acceleration is 0 and mass times zero is zero, so how can weight be a measurement of force.

The answer to this question is hard to explain but I'll give it a shot. We are accelerating by the pull of gravity at an approximate speed of 32.174 feet per second (I'm not going to put squared on here, beyond the scope of this article). What then happens is that there is something below us that applies a counter force otherwise we would fall. In this example it would be the scale applying a counter force with the springs, and the amount the springs retract show us how much force that we are applying. This 32.174 is known as the gravitational acceleration.

So now with acceleration somewhat explained that leaves mass. I'm going to approach this definition from a mathematical standpoint vs. scientific which puts more focus on the atomic structure of the object. One way to illustrate mass is to take the scale and mount it on a wall and then get on a swing set and crash my feet onto the scale at various speeds and see what the scale reads. Once again the scale is measuring force, but this time we attempt to factor out the gravitation acceleration (which is very important!). We could take the number the scale reads and determine my acceleration to compute the mass. Since I weight 150 pounds, if I could decelerate from 1 foot per second to a full stop within that second, the scale would show something like 4.66 pounds? Where the scale is still showing the units in pound-force, but since the acceleration is 1, this exposes the mass value which really is in the unit of slugs using the BG system. 1 lb = (1 slug)(1 ft/s2). What the heak is a slug? It *weighs* the same as the gravitational acceleration 32.174 if converted to units of pound force, and is the BG system solution of defining a unit of mass. Now you could alter the equation and work with pound-mass using the EE system but for me, I'd rather keep the same equation and work with the BG system to keep things simple. However, I personally do not care to deal with slugs, so I use the SI system, where they chose to use kilograms as a unit of mass which weighs about 2.2 pounds. Let me illustrate the difference.

667 = 68.03 * 9.8
150 = 4.662 * 32.174
As shown above, in the BG system we use pounds which are the unit of force, now if the SI system copied they could say you weigh 667 newtons, and actually that is a true statement. However, they actually say you "weigh" 68.03, but keep in mind that weight is a measurement of force and not of mass. Here is the trick, they work with the Newton value first, and then convert this to a unit called Kilogram-force, and yes they are equal to Kilogram-mass as long as the acceleration is equal to the gravitational acceleration. It just so happens to work out this way because of the fact that a meter unit is larger than the foot, and yet the actual weight between the pound and the Kilogram-force are both a suitable unit of weight to manage.

When dealing with physic equations like torque, the idea is to aware is that we deal with force and distance not mass and distance. So the most common measurements that I have come across are: pound-foot, ounce-inch, and newton-meters, where these are all forces. What I've found is that on paper I can stick with foot pounds for a rough draft design, but convert to an SI system in code.

One other way that helps me to understand the difference between Kilogram-mass and Kilogram-force is as follows:
Kgf = (Kgm=Kgf/1) * a if a = g (where g is the gravitation acceleration in mps)
Kilogram force would not be equal to kgm if "a" is at a different rate, because converting from Newton's to Kgf is always by g
lb = (slug=lb/g) * a if a = g (where g is gravitation acceleration in fps)
lb (force) would not be equal to (slug=lb/g) if a is at a different rate;

To illustrate converting from Newtons to Pounds, you could first convert newtons to kilograms (force), and then use the conversion from kgf to lbf which works because both forces are working with the same a=g at that point. Fortunately there is a constant (1/4.44822) for this to avoid using two coefficients. This is really taking the 9.8 gravitation acceleration and dividing by the kgf->lb which is approximately 2.2.