Re: [Phys-l] Coriolis effect puzzlement

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

This is a very difficult idea for students to understand.

Do you know those rotating platforms at playgrounds?  Stand near the end
while it spins.  Do you get dizzy?  Or only if you stand at the center?

P.S. I once made a video of myself seated on a portable rotating
platform that was, in turn, placed near the edge of one of those
playground rotating platforms.  I placed a video camera at the other end
and taped myself as I brought my hands in toward my body and away.

Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@esu.edu    http://www.esu.edu/~bbq 


-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Bob
Sciamanda
Sent: Friday, December 02, 2011 1:09 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Coriolis effect puzzlement

To further bring home the phenomenon at issue here, consider:

A skater stands way off center on a rotating ice rink, partaking only of
the platform motion, and holding weights in her outstretched hands.
If she brings in her arms, will she begin to spin about her platform
position?


From: Bob Sciamanda
Sent: Friday, December 02, 2011 9:26 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Coriolis effect puzzlement To emphasize the
differences between spin/angular momentum calculated about the earth's
axis vs spin/angular momentum calculated about a real or gedanken
arbitrary space pont (at which a future low pressure center might form),
consider two air masses located on the same meridian, a meter or so
apart apart.  In an inertial frame, each has an Easterly directed
velocity, due to their partaking of the earth's spin. Their angular
momenta relative to any point on the earth's axis are in the same
direction and completely additive.  In contrast, their momenta relative
to a gedanken point midway between them (and on their common meridian)
are opposed in direction. The question is, what happens if a low
pressure center develops at the midpoint, causing the air masses to move
toward that midpoint.  The proposed models leading to a localized vortex
seem to sidestep these complications.


From: John Denker
Sent: Friday, December 02, 2011 8:18 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Coriolis effect puzzlement On 12/02/2011 03:50 AM,
Bob Sciamanda wrote:
> John Denker wrote:
>
> "1) Relative to the inertial frame, the earth is observed to spin.
>
> 2) Due to friction, we are not surprised to find that on average, the 
> atmosphere spins along with the solid earth. We take this as a 
> zeroth-order approximation to the actual behavior.
>
> 3) There are various local effects such as uneven solar heating, 
> orography, precipitation (which liberates a lot of latent heat), et 
> cetera. Sometimes these result in a local updraft. This leaves us with

> a local low pressure area.
>
> 4) As the rotating air mass falls into the low pressure area, the rate

> of spin increases. This can be explained in terms of conservation of 
> angular momentum. It can equally well be explained in terms of 
> conservation of linear momentum, in accordance with Newton's third 
> law, if you want to do things the hard way."
> ****************************************************
> There seems to be a lacuna in this chain of reasoning:
> How does spin of an air mass about the earth's axis, stated in (2), 
> become spin about a low pressure center, presumed in (4) ?
> There is lacking a mechanism for STARTING THE SPIN ABOUT THE LOW 
> PRESSURE CENTER.  In the rotating frame this is provided by the
Coriolis effect.
> What is the dynamical mechanism as viewed from an inertial frame?

The dynamical mechanism is called "friction", as explicitly mentioned in
item (2).

Again the rule is you can pick any reference frame you like, but you
can't mix-and-mismatch.  Since you asked me to use an inertial reference
frame, don't be surprised if I use an inertial reference frame.
-- In this frame, the air was spinning before the low
  pressure center formed.  Explanation: friction.
-- Immediately after the low pressure formed, it is
  still spinning.  Explanation: conservation of angular
  momentum.  Also friction.
-- At this point, maybe the air is at rest relative to
  some rotating reference frame, but that is totally
  irrelevant, because we are not using that frame.  We
  are not measuring rotation relative to whatever the
  low pressure center is doing.  The center is an abstract
  point anyway, with zero size, so we can't even tell
  whether or not the "center" is spinning.  Again:  you
  asked me to use an inertial reference frame, so don't
  be surprised if I rigorously stick to using an inertial
  reference frame.  In this frame, the air is spinning.
-- Immediately after the air fell in toward the center,
  that part of the air is spinning faster than before.
  Explanation:  local conservation of angular momentum.

I don't see anything tricky about it.  If you still think there is
something missing, please clarify the question.
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l