Re: non-inertial frames

["A. R. Marlow" <marlow@beta.loyno.edu>]

On Thu, 25 Apr 1996, Mark Sylvester wrote:

> 3. Or does it? In the accelerated frame the body *is* in 
> equilibrium. 

The body is in "acceleration equilibrium" in the accelerated frame
(i. e., all accelerations balance out to zero), but it is clearly not
in force equilibrium as pressure sensors attached to its surface would
show.

> Just as much as my computer monitor is in equilibrium 
> on the table, with the "fictitious" gravitational force counter-
> balancing the thrust of the table. 

Again, all accelerations of your monitor, relative to the frame of the
table, cancel to zero  --  only in that sense is it in "equilibrium."
There is a real unbalanced force on the bottom side of the monitor, and
only on that side, as pressure sensors placed all over the skin of the 
monitor would show.  Thus it is clearly not in a force equilibrium, and 
this exact same force nonequilibrium result would continue to be shown
in whatever reference frame you decide to use for measuring accelerations.
If you use an inertial reference frame (free falling frame) then you 
would find that the acceleration also corresponds to the unbalanced upward
force on your monitor. 
 
> I have become a lot less 
> centripetally dogmatic since starting to include the Equivalence 
> Principle in the course that I teach (by adopting the Cosmology 
> option in the IB Higher Level course). 

The equivalence principle of course has nothing to say about what 
forces your monitor experiences.  It simply says that in a small enough
region of spacetime, you may substitute flat spacetime for curved spacetime
if your accuracy requirements are not too great.

> There was an article a few 
> years ago in Scientific American by Mark Abramovich on the unexpected 
> effects one experiences when orbiting a black hole, which sparked 
> a similar "fugal vs petal" debate. I must have another look at that 
> article.

The article called attention to the surprising and nonintuitive directions
of acceleration that would be found at and inside the event horizons of a
black hole.  The author's terminology was sometime's confusing, but in no
case did his arguments depend on introducing nonexistent forces.
 
> Having said all that, let me add that I think it is entirely 
> appropriate in an introductory course to stick to the inertial 
> reference frame and really to emphasise that in this frame there is 
> no centrifugal force acting on the orbiting body. 

What I think is even more important to emphasize is that IF there is no
centrifugal force in an inertial frame THEN there is no centrifugal force
in any other frame you might chose to use.  Forces do not appear and
disappear at the whim of the observer's choice of a frame of reference for
measuring position, velocity and acceleration!  Forces are well defined
physical phenomena that can be registered and measured objectively and
independently of reference frame by pressure sensors.  If this is 
emphasized, than we don't have to worry about any supposed bugbears
concerning noninertial reference frames, either in introductory courses
or otherwise.  Just tell the truth about noninertial reference frames  --
in them there are accelerations that don't correspond to any forces, and
these accelerations need to be allowed for if one chooses to work in such
frames.  This should cause no problem to anybody, freshman or otherwise.  

 
A. R. Marlow                          E-MAIL:  marlow@beta.loyno.edu
Department of Physics                 PHONE:   (504) 865 3647  (Office)  
Loyola University                                    865 2245  (Home)
New Orleans, LA  70118                FAX:     (504) 865 2453