Re: Coriolis

[Roger Haar <haar@PHYSICS.ARIZONA.EDU>]

Ludwik,
        I think that beside a clear explaination, a clear
description of what the Coriolis effect is.  There are good
videos on this.  (I first really understood the effect in an
intro meteorology class.)  The video is something like
this.  Two people are facing each other on opposite sides of
a turntable, merry-go-round or whatever.  These two are
trying to throw a ball back and forth. A camera is above the
center of the turntable.  IF it is fixed to the ground the
ball goes appears to go straight and the catcher moves away
from the ball.  If the camera is fixed to the turntable, the
ball curves away from the catcher.
        Once it is clear what the effect is, and how it is
reference frame dependent, the theory is easier.

Thansk
Roger Haar
U of AZ

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Ludwik Kowalski wrote:
> I do remember learning about Coriolis force. But this was
> was very long times ago. I never had a chance of teaching
> Mechanics; the Introductory Physics courses I teach are
> never sufficiently advanced to deal with non-inertial frames
> of reference. Here is how I plan to describe the "raison d'etre"
> for this "mysterious" pseudo-force, when I have a chance.
> Please criticize if you see something incorrect in the next
> three paragraphs. Or tell about your approaches. We live on
> a spinning planet and Coriolis forces, as I learned here two
> weeks ago, are responsible for winds. Winds flow along
> the isobars, not perpendicularly to isobars.
> -------------------------------------------------
> Newtonian mechanics was formulated in an absolute frame
> of reference ("the frame of fixed stars"). Its essence can be
> summarized by two general statements. a) All accelerations
> are caused by forces. b) Forces are due to interactions between
> particles (neutral or charged) and depend on distances between
> them. Sometimes forces also depend on relative velocities.
>
> Suppose a particle has an acceleration "a" in the absolute frame.
> Then its acceleration in a noninertial frame will be a+a'. Relative
> distances between particles and relative velocities (ignore Einstein)
> do not change when one goes from one frame to another. This
> implies (see statement b above) that forces between particles remain
> the same. We have a paradoxical situation, forces do not change
> but new accelerations appear. To preserve Newtonian formalism
> we reject the second statement (b). We say that it applies to inertial
> frames only and that in non-inertial frames forces may also appear
> as a result of relative motions of coordinate systems.
>
> The a' component of acceleration did not exist in the absolute
> frame and its appearance is due to a "pseudo-force". This force is
> very real in a rotating frame (it can kill you in a centrifuge) but it
> does not exist in the frame of an inertial observer. Coriolis force is
> one example. It would not be appropriate to type here algebraic
> manipulations (found in many books) which show that an object
> sliding along the radius of a rotating platform (or along a tube in
> a centrifuge) is subjected to two mutually perpendicular pseudo-
> foces: centrifugal m*r*omega^2, and Coriolis,  2*m*v^2/r. Note
> that v in the Coriolis force is the radial speed with respect to the
> rotating platform while v' (in omega=r*v') is the tangential speed,
> with respect to the absolute frame.