From: hees@itp.uni-frankfurt.de   
      
   What I've tried to say is that the equation of motion is always m a = F,   
   valid for basis-independent vectors, which always describe an inertial   
   frame of reference. You cannot describe the equations of motion   
   otherwise, because they must be formulated within the Galilei-Newton   
   model. The "inertial forces" are not "fictitious" but just occur due to   
   the time-dependence of the basis ("rotations" if you use Cartesian ones)   
   and an acceleration of the origin of the non-inertial frame relative to   
   the inertial frames.   
      
   On 25/12/2022 07:34, Julio Di Egidio wrote:   
   > On Friday, 23 December 2022 at 16:09:41 UTC+1, Hendrik van Hees wrote:   
   >> On 23/12/2022 08:24, Luigi Fortunati wrote:   
   >    
   >> The equations of motion of Newtonian mechanics for point particles with   
   >> constant mass are always defined with reference to an inertial frame of   
   >> reference, and you get the equations describing these Newtonian within a   
   >> non-inertial reference frame simply by writing the coordinates of the   
   >> point particles wrt. an inertial frame in terms of coordinates referring   
   >> to a non-inertial frame.   
   >>   
   >> This leads to additional terms when taking the time derivatives.   
   >   
   > Please correct me if I am mistaken, but F=ma is not only valid in inertial   
   > frames, is it?  Indeed, I find the way you are presenting things here still   
   > risks to give the impression that these "fictitious", aka "apparent" forces   
   > are only an artefact of the algebra, while in that sense they are rather a   
   > misnomer for the quite real forces an observer in that non-inertial frame   
   > would feel and measure.  Put simply, if one jumps on a merry-go-round,   
   > fighting the centrifugal force is a real and properly physical thing, no?   
   >   
   > Julio   
   >   
   > [[Mod. note --   
   > 1. Just to be clear: the quoted text was written by Hendrik van Hees,   
   >     not by Luigi Fortunati.   
   > 2. I agree with Hendrik: F=ma (with F only including "real" forces) is only   
   >     valid in an inertial reference frame.  To do Newtonian dynamics in a   
   >     non-inertial reference frame, one must augment F to also include   
   >     fictitious forces (such as the Coriolis force).   
   > 3. From a Newtonian-dynamics-in-an-inertial-reference-frame perspective,   
   >     if I jump on (and hold on to) a merry-go-round, I don't feel a   
   >     centrifugal force.  Rather, the merry-go-round exerts a *centripetal*   
   >     force on me, accelerating me inwards (so that I move in a circle around   
   >     the rotation axis).  The *centripetal* acceleration is what I feel.   
   > -- jt]]   
      
   --   
   Hendrik van Hees   
   Goethe University (Institute for Theoretical Physics)   
   D-60438 Frankfurt am Main   
   http://itp.uni-frankfurt.de/~hees/   
      
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