Re: Centripetal Force vs centrifugal field

[John Denker <jsd@MONMOUTH.COM>]

At 09:17 AM 11/5/99 -0500, Richard Tarara wrote a very thoughtful message:
> The question here is one of nomenclature and pedagogy.

I agree that there are tricky questions of nomenclature and pedagogy, but
there is also some physics hiding here.

> We invent no special name for the net force that causes an object to speed
> up or to slow down.  We simply say that a = (net F)/m either along the
> direction of motion or opposite the direction of motion.  Of course, we have
> no special names for these accelerations either.

That's a good statement of our physicists' point of view.  But
pedagogically speaking, we need to realize that non-experts start out with
the notion that acceleration and deceleration refer (only) to changes in
speed!  It is already a lesson in physics/nomenclature to get them to the
point where they can think about and talk about lateral "accelerations"
that don't change the speed.

> Now with uniform circular
> motion we have a problem.  The acceleration points towards the center of the
> motion but is always changing direction from a Cartesian point of view.

Exactly so.

> It
> is difficult to constantly describe this situation in full, so we use the
> nomenclature 'centripetal acceleration' to make communication 'easier'.

Agreed.  There is nothing special about the centripetal acceleration.
"Centripetal" is just an adjective (like "horizontal") describing the
direction of a perfectly ordinary force.

> Once we've done that, then it is tempting (and has become conventional) to
> call the NET FORCE that causes such an acceleration the centripetal force.

Depending on reference frame, and depending on what one means by NET FORCE,
such a convention could be harmless or it could be nonsense.

> This does balance the more commonly used (outside of physics) term
> centrifugal force, but from the non-accelerating frames you wish to use (and
> I agree you should) such a thing as centrifugal force is non-existent, at
> least in most of the cases where it is usually invoked.

Here's where my thoughts diverge from Rick's.  I teach people to fly
airplanes.  In this situation, it is *entirely* appropriate for the pilot
to use an accelerated reference frame (i.e. the turning airplane).  In such
a frame there is a centrifugal field (I avoid calling it a centrifugal
force) which is just as real as the gravitational field.  The techniques
for doing physics in a rotating reference frame have been known for over
150 years.

If/when someone chooses to use a nonrotating reference frame, that's fine.
But if/when someone else chooses a rotating reference frame, that's fine
also.  Don't say that it is "outside of physics" to do so.

> OK, so what's the problem?  First, you need to dissuade students of the
> notion that there are 'real' centrifugal forces acting.  (Again, so Leigh
> doesn't jump on me, we are considering the normal HS approach of considering
> only inertial frames.)

Again, please don't overstate it.  I happily agree that in a nonrotating
reference frame, there is no centrifugal field.  But please don't go so far
as to say there is no such thing as a centrifugal field.  You wouldn't
believe the sanctimonious email I get from people who discover I've talked
about the centrifugal field in my book.

>  Is it helpful to replace the centrifugal forces with
> centripetal forces?

That's not the issue for me.  As agreed earlier, there is a perfectly
ordinary force which can be described as centripetal.  In the nonrotating
frame this is an unbalanced force resulting in acceleration, and there is
no centrifugal force.  But one can hardly call this a "replacement";  see
next remark for more on this.

> That has been the common pedagogy, but what many of us
> have discovered is that when we do so, students then think of the
> centripetal force AS A FORCE OF NATURE.

Agreed they think that, and agreed it's silly.

There is a special force (or class of forces) resulting from the
centrifugal field, and if centripetal forces are sold as a "replacement"
for centrifugal forces, it's no wonder kids are confused.

> That is, if you ask them to draw a
> force diagram for the person on the Ferris Wheel at the upmost position,
> they would draw THREE forces--the weight of the person pulling down, the
> chair pushing up, AND the centripetal force pulling down.  That is, they
> don't understand that the weight force is greater than the chair force such
> that the net force downwards provides the necessary centripetal
> acceleration.

Agreed.

> In order to address this pedagogical problem, the suggestion has been that
> we NOT use the term centripetal force, but rather the somewhat more
> cumbersome 'net force that causes the centripetal acceleration'.  Doing
> such, at least with introductory students, might prevent the common problem
> detailed above.

That might help, but there is bigger game afoot, as discussed above.

Also.................

At 05:09 PM 11/4/99 -0600, Arlyn DeBruyckere wrote:
>
[students]
> think there is a force directed outward in
> uniform circular motion called a centrifugal force because things go straight
> out from a circle (or so they think - ask them about the release point of a
> football pass or a baseball pitch or anything else that is released from a
> circular sort of motion).

a) In the co-rotating frame, things *are* subject to a straight-out force.
Really they are!  The students are right!

b) Of course in the lab frame they don't fly straight out.

*) My point is that physics teachers must become less intolerant of the
rotating-frame point of view.  About two minutes walk from my house there
is a playground containing a small push-it-yourself merry-go-round.  The
kids love it.  Every three year old in town knows that when you're on the
merry-go-round you feel a centrifugal field.

When physicists say there is no such thing as a centrifugal field it just
makes the physicists look intolerant if not completely foolish.

> Each year I have students do a lab where they first
> calibrate a simple accelerometer (a test tube about 1/2 full of water) using
> linear forces and then put the accelerometer on a turntable.  Many students
> INSIST that their accelerometer is not working because it reads that the net
> force is inward instead of outward.  They don't believe their own eyes.

Ahhhh.  This accelerometer demo is a good one.

It has virtually nothing to do with rotation or with centrifugal force or
the lack thereof.  To see what I mean by that:

Take the accelerometer and set it _vertically_ on the table.  It will
report that it is being accelerated vertically.  The students will be taken
aback by that, also.  The accelerometer indication is backwards from their
usual view that things accelerate downwards (relative to the lab frame).
Of course, from the accelerometer's point of view it is being accelerated
skyward (relative to a freely-falling frame).

So the accelerometer demo is great for teaching people the difference
between "active" and "passive" transformations -- that is, whether we move
the objects in a given reference frame, or move the frame itself.  This
question comes up in the rotating system just as it does in a thousand
different nonrotating situations.

______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com