Re: The old centrifugal force

[Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>]

On Saturday, Nov 15, 2003, Brian Whatcott
described a method of observing, and measuring,
the centrifugal force. He concluded:

> I see it [the result], and I am stationary in the lab
> frame. This force is only available to masses
> which are  accelerating.

Likewise, JohnD wrote:

> Returning to the looping track:  If you look closely
> enough, there will be some sort of spring constant
> associated with the track/wheel system.  If the cart
> tries to push itself "through" the track, the spring
> forces will grow large enough to prevent that.
> Call it a reaction force if you like.

My question was asked in the context trying to
construct a free-body force diagram for an object
sliding counter-clock-wise along a looping track,
for example in the two o'clock location. The first
arrow, representing the force m*g, and pointing
down has already been drawn. What other
arrows must be drawn and how should they be
explain them to students?

1) The diagram MUST SHOW ALL FORCES ACTING
ON THE SLIDING OBJECT. We assume that forces
due to frictional and Coriolis effects are negligible.
Please be specific, I need this for a Monday class.

2) What is the nature of the force acting on the track?
(Am I still allowed to say "what causes it?"). I know
what Millikan say about this force. In the "A First
Course in Physics," copyright 1906, he and Gale
wrote: Inertia manifesting itself in this tendency
of the parts of rotating systems to move away from
the center of rotation is called centripetal force."

Accepting this I would say something like this:

a) the sliding object exerts a force on a track;
it is the force of inertia directed away from the
center (not necessarily along the radius).

b) That centripetal force ("due" to rotation) does
not act on the sliding object. But the spring-like
reaction to that force must be drawn.

c) We draw the second force and give it a name,
such as constrain force, C. The direction of that
force is neither radial nor tangential, for example,
at some angle from the vertical m*g.

d) The net force, R, is the sum of mg and C. The
radial component of R is association (or causing
if you prefer) centripetal acceleration while the
tangential component is "responsible for" the
change in the in the instantaneous speed.

e) The mass of the object was given. Knowing
the radius of the loop, and the instantaneous
speed, one can calculate the centripetal force at
the two o'clock location. Likewise, knowing the
tangential acceleration one can calculate the
tangential component of R.

Is this an acceptable approach? If not then please
provide a better way for explaining the free-body
diagram. The vertical looping road, and a small
friction-free sliding object, offer the most simple
context for dealing with our issues. If we know how
to handle this simple situation we will know how
to deal with more complex problems, such as
equatorial bulging, tides, centrifuges, etc.

3) Yes, the centripetal force is "only a model," like
many other concepts in physics. According to many
old physics books the "cause" of centrifugal force is
inertia (Newton's first law). Who was the first to
declare that the concept of centrifugal force should
not be part of our vocabulary in physics?
Ludwik Kowalski

> At 04:35 AM 11/15/2003, Ludwik, you wrote:

> >  . . . It is not hard to explain that a centripetal force,
> > of some kind, must exist to account for the centripetal
> > (v^2/r) acceleration. But it is hard to identify that force
> > in SOME specific situations, for example, when an
> > object is sliding vertically inside a looping track.
> > If it is not an N3 reaction force then what is it?