Post by Luigi Fortunati Post by Tom Roberts
The adjacent particle on the outside exerts the centripetal force
that constrains the observer to move in a circle...
What you wrote is absurd!
No. What I wrote is correct. You misread and added your own misconceptions.
Post by Luigi Fortunati
The force that the innermost particle exerts on the outermost one
and that that the outermost particle exerts on the innermost one
cannot both be centripetal!
I never discussed that (forces between particles of the string). Forces
between particles of the string are called tension. The string has a
tension that enables its particles to exert a centripetal force on the
observer (because the observer is connected to the string).
Post by Luigi Fortunati
If one is centripetal, the other must be centrifugal, and vice
"Centrifugal force" has a SPECIFIC, WELL DEFINED MEANING IN PHYSICS: one
of the "fictitious forces" that arise in rotating coordinates to permit
one to apply Newton's laws in the rotating coordinates as if they were
inertial. In particular, we NEVER use that term for any other
outward-directed force. You violate this usage, and have confused yourself.
In this physical situation, the observer is tethered by a (massless)
string to a central mounting point, and moves in a uniform circular path
around it. The forces are:
a) the string exerts an outward-bound force of tension on the
central mounting point.
b) the string exerts an inward-bound force of tension on the
c) the central mounting point exerts a reaction force on the
string that is equal and opposite to (a).
d) the observer exerts a reaction force on the string that is
equal and opposite to (b).
These are the only forces in the problem; here they are all referenced
to the inertial frame of the central mounting point. We rarely discuss
(c) and (d) as they are trivial; the pairs (a,c) and (b,d) each satisfy
Newton's third law. Note that (b) is the only force on the observer, and
the acceleration corresponding to it makes the observer move in a
uniform circle around the central mounting point, while the observer and
string rotate around it; that is a basic application of Newton's second law.
If one wants to analyze this using the rotating coordinates in which the
observer and string are at rest, one must imagine an additional
"centrifugal force" equal and opposite to the tension force on the
observer (because in these coordinates the observer is at rest, so must
have zero total applied force) [#]. This is all well known, and the
"centrifugal force" is determined by the rotation of the coordinates and
by the radius and mass of the observer. Note that the "centrifugal
force" is proportional to radius, and thus is zero on the central
mounting point (think about it -- that point is not rotating).
[#] The other "fictitious forces" of rotating
coordinates, the "Coriolis force" and the "Euler
force", are both zero in this physical situation.
[This is getting overly repetitive, and I will not
participate further. Get a good book on Newtonian
mechanics and STUDY IT. Perhaps also read