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.
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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.