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Re: Centrifugal force



On 11/17/2003 08:04 AM, Kilmer, Skip wrote:
I've never really understood Physics teachers' distaste for the
phrase, centrifugal force.

In loose analogy to the discussion about "heat", I
suspect there are two questions hiding there:
-- Terminology: what terms go with which ideas?
(which is a problem since we have at least two
ideas going by the same name), and
-- Physics: which ideas are good or bad?

To dispell part of the terminology problem, I like to
use two different terms:
*) The _radial_ component of some force. If we can
define a radial direction, we can project out the
radial component of our favorite force. This has
to do with e.g. polar coordinates, whether or
not the reference frame is rotating.
*) The _centrifugal field_. This is profoundly analogous
to the gravitational field. It is not a force
field; it is a force per unit mass, which is
properly called an acceleration field. The
centrifugal field arises if-and-only-if you are
working in a rotating reference frame.


Students come into class convinced (as indeed they should
be) that the centrifugal field exists. This comes from
their experience of rotating frames, such as a car going
around a corner at high speed, or (especially) a rapidly
spinning playground merry-go-round.

One obvious problem is that students are often tempted
to use a rotating reference frame before they're ready.
Newton's laws (in the usual form at least) do not apply
in a rotating reference frame. Since we can't teach
everything at once, we start by teaching Newton's laws
in a non-rotating reference frame.

I understand (but don't approve) mistakes such as the
following:
-- A teacher might leave off the last four words in
the following:
"There is no such thing as a centrifugal field
in a nonrotating frame."
^^^^^^^^^^^^^^^^^^^^^^
-- A teacher might leave off the last word in the
following:
"You should not be using a rotating frame yet."
^^^

Doesn't N3 tell us that for every centripetal force on an object
there is an equal centrifugal force on another object?

No, for at least two reasons.
a) Even in a non-rotating reference frame there is a
problem, if/when we have action-at-a-distance
(such as Newtonian gravity) in a non-rectangular
basis-vector system (such as polar coordinates).
The essence of the problem is that the radial
direction "here" is not parallel to the radial
direction "there".
b) Momentum (as usually defined) is not conserved in
rotating reference frames, as we now discuss.

To illustrate point (b), suppose we have a free
particle that is stationary in the lab frame, and
we analyze it in a rotating reference frame (not
centered on the particle). We see the particle
_orbit_ the axis of rotation. It is subject to
the centrifugal field, but the Coriolis effect is
strong enough to not only overcome the outward
centrifugal effect, but also to bend the trajectory
inward to form the orbit. The particle has a
large momentum in a constantly-changing direction.
These momentum-changes are obviously not balanced
by any equal-and-opposite changes elsewhere, since
this particle is the only object in the system.

(Tangent: I have long suspected that if you choose
a reference frame rotating about the center of mass,
you can define a momentum-like quantity that is
conserved even in a rotating frame, but I've never
bothered to work out the details.)

Bottom line:
*) Vectors can be tricky in nonrectangular coordinate
systems, even if the reference frame is nonrotating.
*) Things get even trickier if you have objects sitting
in a rotating reference frame (centrifugal fields).
*) Things get trickier again if you have objects moving
in a rotating reference frame (Coriolis effects).

The required tricks can be learned, and there are many
many cases where it is 100% appropriate to use rotationg
reference frames ... but that's not where you start in
an introductory course.