Re: F=ma

[John Denker <jsd@MONMOUTH.COM>]

At 04:13 PM 11/5/99 -0500, Clarence Bennett wrote:
> > Or V=Ir -- potential "causes" current.
>
> I would prefer V/R=I, to keep the conditions on the side of cause, and the
> result standing alone.
>
> Also,  How about  V/R => I, so to distinguish Causes from Equals.

Oooooo nooooooo.  There seems to be an emerging consensus on this list that
equations have a direction of causation to them.  They usually don't.

> (assuming a voltage source)

But but but but there's not usually a good reason for assuming that.  Not
in anything but a certain subset of trivial circuits.  Even for something
as almost-trivial as a voltage divider (two resistors in series) you can't
assume that.

I say again, most laws of physics express an equivalence which is a
**bidirectional** implication.
   F = ma
just as much as
   ma = F
just as much as
   a = F/m
et cetera.

Feynman goes on for several pages about this in _The Character of Physical
Law_.  You're in for no end of grief if you get this wrong.


========================

An interestingly different story concerns definitions.  If we say A is
defined in terms of B, that by no means is the same as saying B is defined
in terms of A.  I write definitions as
  A := B
to show the asymmetry of the relationship.

If we know that
  A := B,
then we can immediately infer that
  A = B
and
  B = A
but not
  B := A

===========================

In typical problems, some of your forces will be defined in terms of ma,
but others will not.

For instance, it would be a violation of basic rules of logic to write
  F := ma
and
  F := GMm/r^2
because you can't have two definitions for the same thing.

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com