From: tjroberts137@sbcglobal.net   
      
   On 11/12/17 11/12/17   11:58 PM, Luigi Fortunati wrote:   
   > Centrifugal force is an "apparent" force.   
      
   Hmmmm. Rather than "apparent", say "fictitious", because that's what it is -- a   
   FICTION that permits one to apply Newton's laws in rotating coordinates.   
      
   Remember that Newton's laws only apply in an inertial frame. This is ESSENTIAL,   
   and the confusions in this thread are due to people forgetting it.   
      
   Historically people wanted to apply Newton's laws in coordinates fixed to the   
   earth's surface. As the earth rotates, "centrifugal and Coriolis forces" were   
   invented to account for the rotation; they are only important on large scales   
   (> a few km), and were initially invented for long-range artillery.   
      
   	I put "centrifugal and Coriolis forces" in quotes, because   
   	the names are a misnomer -- they are not forces, they are   
   	mathematical conveniences. With the hindsight of GR we   
   	recognize they are certain components of the geometrical   
   	connection projected onto rotating coordinates.   
      
   Here is how you can avoid going wrong about such things: coordinates are human   
   fabrications used for convenience in describing physical phenomena. They are   
   ARBITRARY. As arbitrary human constructs, they cannot possibly affect any real,   
   physical phenomena. That implies that any real phenomena must be modeled by   
   coordinate-independent mathematical quantities (such as scalars, vectors,   
   tensors...) -- any coordinate-dependent quantity cannot possibly be real. Both   
   "centrifugal and Coriolis forces" depend on the coordinates used, and vanish in   
   an inertial frame, so they cannot be real.   
      
   Here's another way to avoid going wrong: for any real force you can figure some   
   way to measure it via a spring scale. For instance, put the scale in line with   
   the rope and measure its tension. For "centrifugal and Coriolis forces' there   
   is   
   no place to put the scale -- it is impossible to measure them.   
      
   	Note this also applies to the "force of gravity" -- there's no   
   	place to put the scale. A bathroom scale measures the force of   
   	the earth pushing you upward, but you cannot measure the "force   
   	of gravity" pulling you down. With the hindsight of GR we   
   	recognize that the "force of gravity" is also fictitious, just   
   	like "centrifugal and Coriolis forces" (i.e. it, too, is certain   
   	components of the connection in non-inertial coordinates).   
   	Note the context of this post is Newtonian mechanics, and you   
   	cannot apply all of what I say here to GR.   
      
   > The sling rotates and the hand exerts a real centripetal force on the rope.   
      
   Yes. The rope transfers it to the stone in the sling, which consequently does   
   not follow a uniform straight line, but rather goes around in a circle. Here   
   I'm   
   implicitly using coordinates fixed to the ground, and the rotation of the earth   
   is negligible, so these are inertial coordinates -- there is no "centrifugal   
   force".   
      
   	If there were a "centrifugal force" in these coordinates, it   
   	would cancel the tension in the rope pulling on the stone, the   
   	stone would have zero net force on it, and would go in a straight   
   	line. But it goes around in a circle.   
      
   You MUST keep track of which coordinates you are using, and which forces you   
   are discussing. You confused yourself by not doing that.   
      
   > For the third principle, even the rope exerts an equal and opposite force   
   > (hence centrifuge) on the hand.   
      
   Yes. But this is NOT "centrifugal force", this is a force of tension in the   
   rope. (More about "centrifugal force" on the hand below.)   
      
   > How is possible that the two opposing forces, one is real and the other   
   > apparent?   
      
   You must keep track of which forces you are discussing. The rope exerts tension   
   on the stone, and tension on the hand -- both are real. In these coordinates   
   fixed to the ground there simply is no "centrifugal force". So the problem   
   you think you see does not really exist.   
      
   If you use coordinates in which the rope and stone are at rest, then a   
   "centrifugal force" arises in these rotating coordinates, it cancels the force   
   of tension on the stone, and the stone does follow a uniform straight line in   
   these rotating coordinates (it remains at rest). This is due purely to the use   
   of non-inertial, rotating coordinates.   
      
   In these rotating coordinates, how about a "centrifugal force" on the hand   
   holding the rope? For the case in which the hand remains at rest at the center   
   of the rotating coordinates as the stone revolves around it, "centrifugal   
   force"   
   is zero because it is proportional to radius from the rotation center.   
      
   Other people have added to the confusion:   
      
   Gerry Quinn said:   
   > In a rotating reference frame [...], centrifugal force exists.   
      
   This is a PUN on "exists". We normally use that word for real, physical objects   
   or phenomena. But "centrifugal force' is a purely mathematical construct, and   
   is   
   not "real" in any sense of the word.   
      
   > ["centrifugal force"] causes objects to move away from the centre of rotation   
   > when they are not subject to any other force.   
      
   This is not true. A mathematical fiction cannot "cause" anything. An object not   
   subject to any force moves in a uniform straight line (Newton's first law,   
   implicitly relative to an inertial frame) -- that is what happens. It's just   
   that such a uniform straight line, when observed via rotating coordinates,   
   LOOKS   
   like accelerated motion attributable to a magic "centrifugal force" (it's magic   
   because an inertial observer does not see it).   
      
   > We can also look at the situation in terms of an inertial reference frame   
   > [...].  Then we see the the centrifugal force as the reaction to a   
   > centripetal force that is causing a body to move non-inertially.   
      
   This is very confused. In an inertial reference frame, there is no "centrifugal   
   force". The reaction to the centripetal force of the above rope pulling on the   
   stone is simply the tension of the rope pulling on the hand. The stone has an   
   unbalanced force (tension of the rope), and thus does not move in a uniform   
   straight line. As I said above, if there were a "centrifugal force" in inertial   
   coordinates, the above stone would have no net force and would NOT go around in   
   a circle -- BUT IT DOES.   
      
   Douglas Eagleson mentioned   
   > oscillative action of the hand [...] airplanes   
      
   This is getting bogged down in details. Your entire post was so focused on   
   minutiae and other physical situations that it is not feasible for me to   
   respond   
   to it. But you also seem to be confused about the reality of "centrifugal   
   force"   
   and the utter impossibility of it to "cause" anything.   
      
   Tom Roberts   
      
   --- SoupGate-Win32 v1.05   
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