Re: Forces w/o third-law partners???????

[John Denker <jsd@MONMOUTH.COM>]

At 10:30 PM 10/20/99 -0700, Leigh Palmer wrote:
> Are you under the impression that vertical components of momentum are
> conserved in the laboratory? If they were, we wouldn't need tables or
> chairs.

1) Our need for tables and chairs provides absolutely no evidence for
nonconservation of momentum.

> If you shift your frame of reference outside and include the
> Earth in your system you might notice that the system is rotating on
> its axis, and that the table has to exert an extra force over and
> above the gravitational force on any object placed on it to accelerate
> the object. That's why the object doesn't move with constant velocity;
> it moves in a circle that it completes in one day.

2) The rotational effects are only a minor perturbation on the plain old
GMm/r^2 gravity -- and indeed the part properly called "centrifugal" is of
the opposite sign.  Therefore it has less than nothing to do with our need
for tables and chairs.  See also item (3) below.

At 11:39 PM 10/20/99 -0400, Bob Sciamanda wrote:
> This is why centrifugal and other inertial forces are called
> "fictitious" in traditional Newtonian mechanics.

3) Strictly speaking, that's not why the centrifugal field is called
fictitious -- because strictly speaking the part called the centrifugal
field (excluding Coriolis effects) *does* conserve momentum.

Obviously, if you have an object with nonzero momentum and rotate the
reference frame, the momentum is not conserved in that frame.  But that's
Coriolis, not centrifugal.  My point, though is that if you have a static
system and choose a rotating reference frame comoving with the system's
center of mass, then the systems total momentum (zero) is conserved even in
the rotating frame.  There are centrifugal forces but they balance.  A
rotation of zero is zero.

But the distinction here may be more terminology than physics.

> The laboratory on the Earth's surface is not an inertial reference
> frame. The vertical component of translational momentum is never
> conserved in the laboratory; conservation of momentum only holds for
> systems on which no external forces act.

That's an overly narrow statement of the principle of conservation of
momentum.  The smart thing to do is include boundary terms:

       d(momentum in a region)/d(t) = - net momentum flowing across
                                        boundaries of the region.
i.e.
        d(P)/d(t) = - div P

This is the 100% standard formulation of a *local* conservation law.

To say the same thing again: the lack of external forces is a sufficient
but not necessary condition for conservation of momentum.

Stating the conservation (of momentum, charge, or anything else) in the
non-local form is next to useless.  It allows any apparent non-conservation
to be weasled away by mere assertion that the disappearing quantity must be
magically appearing "somewhere" else.  But real physics says that
"somewhere" isn't good enough.  It has to cross the boundary of the region.


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