Re: [Phys-l] Coriolis effect puzzlement

[John Denker <jsd@av8n.com>]

On 12/01/2011 05:18 PM, Robert Cohen wrote:
> I just want to point out one thing that some people seem to be glossing
> over here: on the non-inertial frame of the rotating earth, the
> centrifugal effect is *not* observed 

We agree that in this context we don't need to explicitly
account for the centrifugal field.

> because, for the Earth, the
> centrifugal effect is balanced by a *centripetal* force.

Well, that's one way of looking at it ... but it's not practical
and not conventional.  I don't recommend it.

As we discussed a couple of weeks ago, a simpler way to explain
the ordinary laboratory reference frame is to say that the
centrifugal field has been lumped into the conventional definition
of the gravitational field, g.  This affects the magnitude of the 
g vector and also the direction, i.e. the conventional definition 
of "vertical" and hence "horizontal".

So it might be better to say the the centrifugal fields is not
*separately* observed, not *explicitly* observed.  Instead, it
is implicitly observed as part of the conventional, practical g.

Considering the centrifugal field as part of the local g field
makes perfect sense, to first order, in accordance with Einstein's
principle of equivalence.  Specifically, it makes sense to a good
approximation on ordinary classroom length-scales and time-scales.
On longer scales, everything works fine in the laboratory frame
provided you also include the Coriolis terms.

Terminology note:  In engineering, including aeronautics, people
often speak of an ECEF frame : an earth-centered earth-fixed 
frame.

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

This creates a slight moral hazard in the introductory physics
class.  

There are good reasons why we start with inertial reference frames.
Rotating frames are considered "beyond the scope of the course".

Meanwhile:
  a) Practical considerations demand that we use the laboratory
   reference frame.
  b) Practical considerations demand that we include the the
   centrifugal field in the conventional definition of g.
  c) Therefore we *are* using a non-inertial reference frame,
   even though the understanding of such things is beyond the
   scope of the course.

Theoretically speaking, this state of affairs is illogical and
self-inconsistent.  There is no logical way to include the
centrifugal field without also including the Coriolis effects.
   In practice, you can get away with this to a reasonable 
   approximation, on ordinary laboratory length-scales and 
   time-scales, provided you don't look too carefully at the 
   data.  
Still, there are always things like Foucault pendulums and 
meteorology and astronomy to remind you that the laboratory 
frame is *not* an inertial frame.  Even after you have 
accounted for the centrifugal field, an ECEF frame is 
definitely not an inertial frame.