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Re: Centrifugal force



1) The "conical pendulum" is a fine pedagogical
example.
-- Another name for this is "tetherball".
-- It is a slight generalization of the basic
"centrifuge" geometry.

2) Some students are confused by this because it
involves continual acceleration. Some students are
still stuck in the static rut ... they expect all
forces to balance ... they _want_ all forces to
balance.
-- Sometimes this drives them to implicitly or
explicitly switch to a rotating coordinate system,
in which the forces actually do balance ... but
they may not be able to afford the cost of doing
this, namely the invalidity of Newton's laws in
the rotating frame.
-- Sometimes this drives them to draw a just-plain-wrong
force diagram.

3) As a possibly related point, there is sometimes
confusion about the distinction:
-- the action=reaction balance at the string/ball
interface in accordance with the third law, versus
-- the overall imbalance of forces that leads to
acceleration of the ball in accordance with the
second law. It's hard to see how there can be
*any* net force, if all the forces cancel in
pairs according to the third law.

It should be rather sobering to read the posts in
this thread to see how hard professionals have to
work to express this distinction. It's hardly
surprising students struggle with it.

Possibly constructive suggestion: Whenever I'm
faced with a situation like this, I de-emphasize
the notion of force and rely on the notion of
_momentum_. I can vividly visualize momentum
pouring across the string/ball boundary.

To illustrate this approach in all its glory,
consider a chain, with one end fixed while
all the rest swings around in a circle. For
simplicity we neglect gravity (but you can
always add that back in if you want). There
are N links, each with 1/Nth of the total mass.
In each unit of time, momentum p01 flows from
the pivot-structure into link #1. Similarly
momentum p67 flows from link #6 into link #7.
Momentum p78 is less than momentum p67, because
some momentum gets left behind in link #6 to
give it the acceleration needed to maintain
circular motion.

I am quite aware that everything in the previous
paragraph can be restated in terms of forces,
but I find it easier to visualize in terms of
momentum. Also I find that the momentum version
helps me avoid questions about what is "The"
force at the #6/#7 boundary.

(Tangential note: interactions such as tension
in a string or pressure involve transport in
the X direction of the X-component of momentum.
In contrast, there are interactions such as
shear, e.g. sliding friction, that involve the
transport in the Y direction of the X-component
of momentum. Again this can all be formulated
in terms of forces, but I have an easier time
visualizing the momentum. I see a little vector
labelled "p" hopping across the interface.)

(More-important note: the momentum formulation
generalizes nicely to
-- special relativity,
-- general relativity, and
-- fluid dynamics (including rain falling on railcars),
where it is usually much harder and sometimes quite
impractical to describe what's happening in terms
of forces.)

On 11/17/2003 01:52 PM, Robert Cohen wrote:
If, as it appears from this list, physicists automatically interpret
"centrifugal" to mean the "outward-pointing <something> associated
with observing objects in a rotating reference frame"

That's a common and not-unreasonable interpretation.

> then IMHO we've messed up a particular good pair of adjectives.

IMHO it's not a tragic loss, since we have other
terms (e.g. "radial component") that serve
perfectly well to describe the radial component
if that's what's intended.