Re: centrifugal force (cont)

["John S. Denker" <jsd@MONMOUTH.COM>]

From: "Clarence Bennett"

> > When I'm on the turntable, I seem to feel a centrifugal force only as
> > long as I also experience centripetal friction holding me.
> > If I let go, I no longer feel either.

1) That is a very tricky puzzle, not suitable
for presentation to beginning students,
except perhaps as a cautionary tale about
what sort of arguments to avoid.

The problem is that it involves changing
reference frames in mid-sentence:  First
we have "the" observer attached to the
rotating reference frame, and a moment
later we have "the" observer detached.

It would be wiser to analyze this situation
using two clearly-distinguished observers.

2a) According to observer Moe, permanently
attached to the turntable, you are subject
to a centrifugal acceleration (force per
unit mass) whether you are holding on or
not.

2b) According to observe Joe, permanently
situated in the nonrotating laboratory
frame, you are not subject to any centrifugity,
whether you are holding on or not.

3) Does anybody reeeally think that
centrifugity violates the 3rd law?

Remember, centrifugity is no less real
than gravity.  Do you think that gravity
violates the 3rd law?

Let's work it out.  You are hanging on
to a high-dive board, and then you let
go.  According to observer Doe, in a
freely-falling frame, you are not subject
to gravity whether you are holding on or
not.  While you are holding on, you are
accelerated upward by the holding-on
force, and that's the whole story.

According to observer Joe, in the gravity-
infested laboratory frame, you are subject
to gravity whether you are holding on or
not.  While you are holding on, the gravitational
force mg is balanced by the holding-on force.

Joe knows you are subject to gravitational
force even while falling, because he sees
your momentum changing.  He doesn't need to
know anything about "interactions" to know
that your momentum is changing.

If Joe investigates thoroughly enough, he
will find that momentum flowing into you
is matched by an equal amount of momentum
flowing out of the earth.  Joe may or may
not understand the details of how this
momentum flows though empty (and non-empty)
space to get to you.

Does anybody reeeeally think that centrifugity
is any different?

According to Moe, permanently attached to
the rotating reference frame, you are subject
to centrifugity whether you are holding on
or not.  While you are holding on, the
centrifugal force is balanced by the
holding-on force.

Moe knows that you are subject to centrifugal
force even after you let go, because he sees
your momentum changing.  He doesn't need to
know anything about "interactions" to know
that your momentum is changing.

If Moe invesigates thoroughly enough, he will
find that momentum flowing into you is
matched by an equal amount of momentum
flowing out of the merry-go-round.  Moe may
or may not understand the details of how this
momentum flows through empty (and non-empty)
space to get to you.

Let's do an example.  Suppose that before you
let go, the merry-go-round is perfectly balanced,
perhaps because a friend of equal mass is holding
on at the antipodal point.  If you let go and
your friend doesn't, the merry-go-round will be
out of balance.  Moe will observe the earth
pushing on the spindle.  This force on the
spindle is exactly enough to enforce the 3rd
law, balancing the force on you as you accelerate
under the influence of centrifugity.

In other scenarios, for instance if your
friend lets go at some point, the details of
how the 3rd law is enforced will be different,
but still it will be enforced.  If you ask
me exactly _how_ the momentum is transferred
from your friend to you, I will say "hypotheses
non fingo".

Do you reeeally think centrifugity is different
from gravity?

=========

4) It is perfectly possible for me to calculate
the centrifugal acceleration and hence force
without necessarily knowing how many friends
you have or what they are doing.  Force need
not be defined in terms of interactions.

I guess I'm taking the viewpoint that if I can
measure the force, it's a force.  Percy W.
Bridgman had something to say about this.

In a _static_ situation is is usually easy to
pair off the forces, but there's more to physics
than statics.