Re: [Phys-L] apparent weight

[John Denker <jsd@av8n.com>]

I installed more and better diagrams at:
  https://www.av8n.com/physics/tides.htm

I also added a section on why the rotation of the earth has
no effect on the tides:
  https://www.av8n.com/physics/tides.htm#sec-sloffugal

The punch line is:

> We can summarize the situation by emphasizing the distinction between
> spin and orbital motion. The spin gives rise to a centrifugal field
> that has no effect on the tides because it is the same over all
> time. The orbital motion gives rise to a sloffugal field that has no
> effect on the tides because it is the same over all space.

That's the answer to a nontrivial question.  The fact that
the answer is zero does not make the question any less
important.

The center of the earth is not a freely-falling inertial frame. 
In fact, it orbits the CM once a month.  This is is not a small
effect.  You can show that it has no effect on the tides, but
you have to actually show it;  you can't just assume it.

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

Random remark:  Despite the Subject: line of this thread, I
don't recommend the term "apparent" weight.  I just call it
"weight".  Either it's weight or it's not.  Weight is mg,
where m is the mass and g is the acceleration of the chosen
reference frame.
  https://www.av8n.com/physics/weight.htm#sec-def

Weight = mg is also what would be reported by an ideal scale.
This defines what we mean by ideal scale.  This gives us
consistency, but it doesn't tell us much we didn't already
know ... although it does remind us that when using a force 
meter to determine weight, we need to correct for buoyancy.

So, again: weight = mg.  All the effort goes into figuring 
out what g is.

This brings us to a point that virtually every introductory 
textbook gets wrong, namely the definition of "gravity".
The problem is, there are two inequivalent definitions 
floating around.

  g = G M / r^2    (the law of universal gravitation)

  g = the acceleration of a free particle, relative to
      some chosen reference frame.

The second definition is obviously completely frame-dependent,
while the first definition is completely frame-independent.

You can't make the problem go away by assuming some "conventional"
reference frame.  In one chapter, for studying the orbit of the
moon or studying the tides, it is "conventional" to silently
assume an earth-centered non-rotating frame.  In another chapter,
for all terrestrial purposes including architecture, sports, et
cetera, it is "conventional" to silently adopt the lab frame,
which contains smallish but nontrivial centrifugal contributions.

No wonder students are confused.

Even at the level of "conceptual" physics, the concepts here
are dramatically different:  Either gravity depends on mass,
or gravity depends on the acceleration of the reference frame.
You can't have it both ways.

I say authors should be allowed to define things however they
like, but you only get to do that once.  It's not nice to
switch back and forth.

Constructive suggestion:  Is it possible to untangle the mess
by giving different names to the two different notions.  I
call them "barogenic" gravity (δg) and "frame-relative" aka
"framative" gravity (g).  For details, see
  https://www.av8n.com/physics/weight.htm#sec-various-notions