From: tjoberts137@sbcglobal.net   
      
   On 3/17/23 8:13 AM, Luigi Fortunati wrote:   
   > Tom Roberts il 13/03/2023 05:34:17 ha scritto:   
   >> 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.   
      
   > 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).   
      
   > If one is centripetal, the other must be centrifugal, and vice   
   > versa.   
      
   "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   
         observer.   
      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   
   	 https://en.wikipedia.org/wiki/Centrifugal_force]   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)