Re: Centrifugal Force

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

A. R. Marlow expressed his amusement regarding:

> I was amused to read the comment of William Osgood ( Late Professor at
> Harvard) in his "Mechanics" (1937, republished by Dover in 1964) on those
> who insist on imagining an outward force on a particle held in circular
> motion by a string: "There is no answer to these people.  Some of them are
> good citizens.  They vote the ticket of the party that is responsible for
> the prosperity of the country;  they belong to the only true church;  they
> subscribe to the Red Cross drive  --  but they have no place in the Temple
> of Science; they profane it."  

I wonder if there is not some confusion here.  Barring the physics-
challenged masses and many confused introductory physics students, I have
not heard anyone (with a proper physics education) claim there was an
outward force on a particle held in circular motion by a string.  If the
description is of a revolving particle then we seem to be using an inertial
frame and there is then, clearly, no such outward force.

OTOH, if the particle is not revolving but is at rest at one end of the
string, and the whole external world is revolving around the anchor point at
the other end of the string then there is apparently an outward force
pulling on the mass.  The inward force on the mass from the string tension
then cancels this frame-induced force thus keeping the mass at rest.  This
is the case only when we consider a force on an object as something that
acts to tend to change the state of motion of that object, and we consider
forces necessary in order to cause the state of motion of objects to change.

If, OTTH, (on the 3rd hand) we consider a force to be something else
and/or if the state of motion of objects naturally tend to change without
cause (in a noninertial frame) then we still can avoid invoking this
outward force.  In this case we just make do with a world where objects just
naturally accelerate outward from the string's anchor and world's revolution
axis at a rate of r*[omega]^2 where r is the object's distance from this
axis and [omega] is the angular revolution rate of the outside world.  We
also notice that objects in this frame deflect as they move with an
acceleration along the cross product of the object's velocity with the
angular velocity vector of the outside world.  In this description the
mass on the end of the string does not accelerate even though there is a
net inward force from the string tension acting on the mass.  Different
strokes for different folks.  

I find the reference to the excommunication of people from "the Temple
of Science" for profaning it to be somewhat disconcerting.  I think science
ought not be an object of worship, nor a religion (especially an intolerant
one).  It is not possible to profane that which is not holy.  It seems to
me that the topic of "fictitious" forces does seem to bring out the true
believer in people though.  Rather than bar people from science who think
that an outward force is exerted on a revolving mass on a string and
writing them off by saying there is no answer for them, I think even such
deluded ignorant, yet apparently functional, people are educable--if we
just keep trying with the means at our disposal.

> As I said, I was amused;  I do not necessarily agree with the polemical
> language.  A better solution, it seems to me, would be to discuss what we
> all agree on, namely, the accelerations involved.  Everyone agrees that
> there are centrifugal accelerations and Coriolis accelerations relative to
> noninertial frames of reference.  Can't we all just divide by mass and
> discuss accelerations?

I like this attitude/proposal much better than that displayed by the above
quote.  (Can't we all just get along?  :-)   )

>                        All the calculational advantages claimed are
> immediately available.  Then, those who have some "mystical" further
> commitment to inventing forces with non-Newtonian or non-Einsteinian
> properties can go off to their corner and discuss such;  the rest of us
> can go on without such extra "forces."

I don't know if it is so much a commitment to inventing mystical forces, as
it is the absence of a rigid doctrinaire commitment to one particular
absolute true definition of a true force.  It is rather a holding to a looser
concept of a force based on utility and functional role in the mathematics
of a given description of the situation.  Actually, it is the invention of
those extra forces that keeps things a little *more* Newtonian than
otherwise in accelerated frames.  Not calling the frame-induced effects
forces results in both Newton's first and second laws being violated while
preserving the third law (to only the approximate extent it was valid in the
first place).  But referring to these effects as forces preserves *both* the
first and second laws while sacrificing the only the third.  (Relativistic
effects violate both the 2nd and 3rd laws to the same order in 1/c^2 even in
inertial frames, anyway.)

>                                        It seems to me this would clarify
> things a whole lot for our students.

Maybe it would.  Sometimes obediently accepting the received dogma is
easiest.  Certainly many/most introductory physics problems are simplest to 
formulate in an inertial frame where such extra forces do not appear.  This
is not the case when doing problems involving Newtonian gravitation,
however.  When analysing orbital mechanics problems it is simplest to treat
the problem from a (noninertial) frame where the massive body is at rest and
is considered a source of a (locally fictitious on a small scale)
gravitational field, rather than treat the orbits of objects in a frame in
which those objects are unaccelerated in free fall.  Certainly analysing the
behavior of atmospheric and oceanic currents in meteorology and oceanography
is easiest in noninertial frame in which the earth's surface is at rest.

David Bowman
dbowman@gtc.georgetown.ky.us