Do physics equations work in non-SI units?

All unit systems are arbitrary conventions. If you measured acceleration in furlongs per fortnight squared, and you wanted force in pounds, appropriate units of mass could be derived from F = ma. Physics formulas represent general laws derived from observation or calculation.

In the imperial system, there are pounds mass and slugs. A weight of 32.2 pounds in a gravity field where g = 32.2 ft/s^2 equals a mass of 1 slug, or m (slugs) = weight / g. By definition, 1 lbm = 453.6 grams.

Some physical properties have only SI definitions (like volts, amps, coulombs, and such where there are no non-SI units of measurement).

 

What about gauss, statcoulombs, etc., the units of the cgs system?

 

Most equations work no matter what units you use. However, many electromagnetic equations change depending on what units are used.

In your case, you can use F=ma to get the force in units of pounds[mass]*ft/s^2. One problem with imperial units is that force is usually measured in pounds[force], and you need a conversion constant to go from pounds[mass]*ft/s^2 to pounds[force] since they are totally different.

 

Of course. Newton's second law says force is proportional to rather than equal to the product of mass and acceleration. Newton viewed force as some distinct quantity and his second law as a law of nature.

The modern view is that F=ma is a definitive statement rather than a law of nature: It defines force as a derived unit. From this perspective, imperial units, with force in pounds force, mass in pounds mass, and acceleration in feet per second squared, form an inconsistent set of units.

However, from this perspective, SI units are not consistent either. We have to write E=mc² (better: E²=(mc²)²+(pc)²). If SI truly was a consistent set of units we would write that as E²=m²+p². That c is not 1 *and unitless* means that the International System is an inconsistent set of units. The same goes for F=GMm/r². A consistent set of units has G=1, and once again, unitless.

 

I should have said 'Metric' system to cover its many different flavors.

 

they work in any unit just need to but good constants
you can derive 1000's equations of motion using units like pound
in main equation like

F=ma
1 N →1000 mN (millinewton)
1 kg → .....pounds

put it in
metric equation to get some other equation

 

It should be noted that while units generally don't matter for fundamental equations in physics and math, they CAN make a difference for angles. The derivative of sin(theta) is not cos(theta) if theta is measured in degrees rather than radians!

 

On a side note: that c is not unitless in the SI, simply means that according to the SI length is physically different from time. [added:] However, indeed c and G could have been given the value 1.

 

People don't use it much, but the English system actually had a unit of mass, the slug, which was defined so that 1 pound (force) = 1 slug * 1 foot/second^2. So a slug weighs 32 pounds on Earth.

http://en.wikipedia.org/wiki/Slug_(mass)

 

Yes, of course it works, this is like asking does mathematics work in another base system, of course it does.

 

The original poster specifically asked "will a proportionality constant need to be introduced to the equation?" Depending on how the basic units are defined, you certainly do need to introduce proportionality constants in some cases.

 

I don't see how SI units are inconsistent. It's not like you're required to set c=G=1. Planck units are just a convention that physicists find convenient to work with. You won't get a contradiction if you work in SI units.

 

"Inconsistent" doesn't mean you get a contradiction. It's quite possible to do physics and engineering with customary units. One just needs to use F=kma. That is inconsistent with the modern view that force per se is a derived unit. SI has attacked but one of those old, inconsistent views of units. That one has to use c² in E²=(mc²)²+(pc)<sup>2[/sup means that SI is inconsistent with relativity, which says that mass is a form of energy.

Another example: One way to look at the the Lorentz transform is that it represents a hyperbolic rotation in Minkowski space. If one looks at time and distance as fundamentally different things, this view of the Lorentz transformation can only be viewed as a trick, an abuse of notation that happens to work. On the other hand, this is a very natural result if one looks at time and distance as different aspects of the same thing. c should not have any units, and a value of one is the one value that is results in consistent physics.</sup>

 

Force is a measure of mass and acceleration according to classical physics, and mass is a measure of energy content according to relativity. Also, for centuries weight was used as a measure of mass (and bathroom scales still use that). Proportional doesn't mean identical.

 

I don't think it's quite fair to view Newton's "F = ma" as a definition. Without ever measuring any accelerations, one could imagine coming up with a concept of force, in terms of how much weight various "pushes" and "pulls" can lift. With springs and ropes and pulleys and so forth, you can develop an entire science of "static" forces without ever thinking to connecting it to acceleration. This might be a counterfactual (because I have no idea to what extent the concept of "force" was used for static calculations prior to Newton), but one can certainly imagine developing a theory of forces without ever realizing that there is a simple relationship between forces and acceleration. In that case, "F = ma" would be a discovery about the effects of forces, rather than a definition.

 

I agree, I only hinted at that because I already mentioned another issue with a side topic.
And I think that impressive force was already characterized by means of Hooke's law.
Now the discussions have gone in all directions but the OP hasn't given any feedback yet...

 

Many people use the word "consistent" to mean "free of contradiction". That's certainly how it's used in mathematics.

 

That isn't how it's used in the context of determining whether a set of units is consistent. The issue here is whether the system of units is consistent with modern physics. F=kma is not while F=ma is.