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Re: [Phys-l] force or mass



On 11/09/2008 12:22 PM, John Mallinckrodt wrote:

While I understand and appreciate the intent here. I contend that
one can and, more importantly should write F = ma and other laws of
physics* without embedded conversion factors as I will explain below.

That's nice work if you can get it ... but in the world
I live in, there are lots of equations with nontrivial
factors out front, and the factors are nontrivial.

As a particularly infamous example, there are N different
ways of writing the Maxwell equations. Depending on what
units you use for the fields and charges, you can make some
or all of the coupling constants disappear from the equations.

There is AFAICT no consensus on which version is best.
Conventions that simplify one problem complexify another
and vice versa.

As another infamous example, there is a 4pi that shows
up when applying Gauss's law to a point charge that
does not show up when applying Gauss's law to a point
mass, because of a difference in how the fundamental
field equations are _customarily_ written. That makes
the capacitor law particularly simple for electrostatics,
but then there is a 4pi that shows up in the corresponding
law for gravitation. You pays your money and you takes
your choice.

It must be emphasized that there is no easy way out of
this choice. There is no win/win solution. You can't
make the parallel-plate capacitor be simple and also
make the spherical capacitor be simple ... because you
can't set the area of a sphere equal to unity. There
are 4pi steradians on the surface of a sphere, and
there's nothing you can do about it. That 4pi has got
to show up *somewhere*.

...

* There are some, IMO, very unfortunate lapses that have become
common usage.

It seems to me that lapses are the rule rather than the
exception.

The unsophisticated way to look at it would be to say that
we got lucky with F=ma and V=IR which are simple. But as
I see it, it's not luck; it's just a choice. We choose
to make the F=ma law simple. But then the law relating
mass and weight is not as simple as it could be. We could
make both laws simple by choosing units such that g=1, but
that would make /other/ laws more complicated.

The general case looks to me like a whack-a-mole game that
is not worth playing.

Specific cases are another story entirely: It is standard
good practice to choose "scaled units" appropriate to the
problem at hand. For example, in fluid dynamics this
approach leads to analyzing the problem in terms of a
dimensionless coefficient of lift, a dimensionless coefficient
of drag, a dimensionless Reynolds number, et cetera.