Existence of "apparent" force

[Luigi Fortunati]

The "apparent" force exists in the accelerated frame but does not exist
in the inertial frame.

For example, in the case of the slingshot, the (apparent) centrifugal
force exists in the rotating frame.

Does this mean that (in the rotating reference) there really is a
centrifugal force acting on the stone or do we imagine that there is
but, in reality, it isn't there at all?

Obviously, in the second case, no one would ever think of asking to
which fundamental force it belongs but, in the first case, if a force
really acts on the stone, we should be able to establish what kind of
force it is.

Well, is the apparent centrifugal force that really acts on the stone
during the rotation and in the rotating reference part of one of the 4
fundamental forces?

[[Mod. note -- No. The apparent centrifugal force is an artifact of
working in non-inertial (in this case rotating) coordinates. -- jt]]

[Richard Livingston]

Post by Luigi Fortunati
The "apparent" force exists in the accelerated frame but does not exist
in the inertial frame.

...

Post by Luigi Fortunati
Does this mean that (in the rotating reference) there really is a
centrifugal force acting on the stone or do we imagine that there is
but, in reality, it isn't there at all?

...

It is easy to tell the difference between a real force and fictitious forces
due to an accelerating reference frame. Ask yourself if an observer riding
on the object would feel the force. If not it is a fictitious force.

Alternatively, use an inertial reference frame to describe the motion of
the object. If it is still accelerating in that frame it is a real force,
otherwise it is fictitious.

Rich L.

[Luigi Fortunati]

Post by Richard Livingston

Post by Luigi Fortunati
The "apparent" force exists in the accelerated frame but does not exist
in the inertial frame.

...

Post by Luigi Fortunati
Does this mean that (in the rotating reference) there really is a
centrifugal force acting on the stone or do we imagine that there is
but, in reality, it isn't there at all?

...
It is easy to tell the difference between a real force and fictitious forces
due to an accelerating reference frame. Ask yourself if an observer riding
on the object would feel the force. If not it is a fictitious force.
Rich L.

Right.

An observer riding any particle of the string or sling stone feels the
centripetal force of the innermost adjacent particle and the
centrifugal force of the outermost adjacent particle.

If so (and it seems to me that it is) both of these forces are real and
there are no fictitious forces anywhere (of the spinning slingshot).

Luigi.

[Tom Roberts]

Post by Luigi Fortunati
An observer riding any particle of the string or sling stone feels
the centripetal force of the innermost adjacent particle

Yes.

Post by Luigi Fortunati
and the centrifugal force of the outermost adjacent particle.

Nope.

In the inertial frame of the center their path is a circle with an
acceleration 3-vector pointing to the center of rotation. It is clear
there is no acceleration away from the center, and therefore no force on
the observer in that direction.

In coordinates rotating with the observer, the observer is motionless,
with zero acceleration. In these coordinates a FICTITIOUS "centrifugal
force" arises that cancels the real centripetal force.

"Centrifugal force" IS fictitious. It is due PURELY to choice of
coordinates, and thus cannot model any real, natural phenomenon.

Post by Luigi Fortunati
(again in the
rotating reference) there are neither centrifugal nor centripetal
accelerations.

Yes, because the FICTITIOUS "centrifugal force" that appears in the
rotating coordinates cancels the real centripetal force, giving a net
force of zero IN THESE COORDINATES, and ONLY in these coordinates.

[I repeat: a quantity that depends on coordinates, like
"centrifugal force", cannot possibly model a real,
natural phenomenon, because nature uses no coordinates.
Ditto for the other fictitious forces...]

Tom Roberts

[Luigi Fortunati]

Post by Luigi Fortunati
An observer riding any particle of the string or sling stone feels
the centripetal force of the innermost adjacent particle

Yes.

Post by Luigi Fortunati
and the centrifugal force of the outermost adjacent particle.

Nope.

Nope? If you put yourself in the shoes of any particle of the string or
stone, do you feel that the innermost adjacent particle pulls you
towards the center and don't you feel that the outermost adjacent
particle pulls you to the opposite side?

...
"Centrifugal force" IS FICTITIOUS and appears in the rotating coordinates...

"Appears" in what sense?

Does it appear in the sense that we "see" the force appear?

And how is this apparition manifested?

Can it be observed or measured?

Or is it just supposed to be there?

I would like to know not in the abstract but in the concrete and real
case of the spinning slingshot.

Tom Roberts

Luigi.

[Sylvia Else]

Post by Luigi Fortunati
The "apparent" force exists in the accelerated frame but does not exist
in the inertial frame.
For example, in the case of the slingshot, the (apparent) centrifugal
force exists in the rotating frame.
Does this mean that (in the rotating reference) there really is a
centrifugal force acting on the stone or do we imagine that there is
but, in reality, it isn't there at all?
Obviously, in the second case, no one would ever think of asking to
which fundamental force it belongs but, in the first case, if a force
really acts on the stone, we should be able to establish what kind of
force it is.
Well, is the apparent centrifugal force that really acts on the stone
during the rotation and in the rotating reference part of one of the 4
fundamental forces?
[[Mod. note -- No. The apparent centrifugal force is an artifact of
working in non-inertial (in this case rotating) coordinates. -- jt]]

If an observer is in a rotating frame, but fails to take account of
that, and instead seeks to explain the behaviour of freely moving
objects as if the observer were in an inertial frame, the observer then
has to invent the centrifugal force.

So the force is not real. It arises from a mistaken world-view.

Sylvia.

[Luigi Fortunati]

Post by Luigi Fortunati
The "apparent" force exists in the accelerated frame but does not exist
in the inertial frame.
For example, in the case of the slingshot, the (apparent) centrifugal
force exists in the rotating frame.
Does this mean that (in the rotating reference) there really is a
centrifugal force acting on the stone or do we imagine that there is
but, in reality, it isn't there at all?
Obviously, in the second case, no one would ever think of asking to
which fundamental force it belongs but, in the first case, if a force
really acts on the stone, we should be able to establish what kind of
force it is.
Well, is the apparent centrifugal force that really acts on the stone
during the rotation and in the rotating reference part of one of the 4
fundamental forces?
[[Mod. note -- No. The apparent centrifugal force is an artifact of
working in non-inertial (in this case rotating) coordinates. -- jt]]

If an observer is in a rotating frame, but fails to take account of that, and instead seeks to explain the behaviour of freely moving objects as if the observer were in an inertial frame, the observer then has to invent the centrifugal force.
So the force is not real. It arises from a mistaken world-view.
Sylvia.

The "apparent" centrifugal force you mention (the one needed to explain
the behavior of a moving object by an observer who is in an accelerated
reference) is good for the case of the lighter on the dashboard of the
car when cornering, where the lighter moves.

On the other hand, the rope and stone of the sling do not move (in the
rotating reference).

So, your definition is not good for the slingshot, because (again in the
rotating reference) there are neither centrifugal nor centripetal
accelerations.

The string and the stone rotate only in the inertial reference but not
in the accelerated one.

Luigi.

[Tom Roberts]

Post by Luigi Fortunati

Post by Luigi Fortunati
An observer riding any particle of the string or sling stone
feels the centripetal force of the innermost adjacent particle

Yes.

Post by Luigi Fortunati
and the centrifugal force of the outermost adjacent particle.

Nope.

Nope? If you put yourself in the shoes of any particle of the string
or stone, do you feel that the innermost adjacent particle pulls you
towards the center and don't you feel that the outermost adjacent
particle pulls you to the opposite side?

The adjacent particle on the outside exerts the centripetal force that
constrains the observer to move in a circle. There is no force exerted
by the adjacent particle on the inside, because the string is in tension
and is incapable of exerting an outward force.

Note also that "centrifugal force" is fictitious and appears only in the
rotating coordinates. It cannot ever be "felt" by an observer, because
it is not real (in any sensible sense of the word).

Remember that no coordinate-dependent quantity can model any real
phenomenon in the world we inhabit, because nature uses no coordinates.
(Coordinate dependence would mean that multiple calculated values would
all have to be equal to the single value of nature.) We humans use
coordinates to describe and model the world -- they are an arbitrary
construct of humans; coordinates are imaginary, though clocks and rulers
used to implement them are real.

Post by Luigi Fortunati

"Centrifugal force" IS FICTITIOUS and appears in the rotating
coordinates...

"Appears" in what sense?

In the sense that one must include it in order to apply Newton's laws in
those rotating coordinates.

Post by Luigi Fortunati
Can it be observed or measured?

No. One can measure the (centripetal) force of tension in the string by
placing a spring scale in the appropriate place. Such a scale cannot
measure the "centrifugal force" on an object because there is no place
to put its other end.

Post by Luigi Fortunati
Or is it just supposed to be there?

If one wants to calculate in the rotating coordinates, one must include
the "centrifugal force" -- otherwise Newton's laws to not describe what
happens.

Tom Roberts

[Luigi Fortunati]

Post by Tom Roberts

Post by Luigi Fortunati

Post by Luigi Fortunati
An observer riding any particle of the string or sling stone
feels the centripetal force of the innermost adjacent particle Yes.
and the centrifugal force of the outermost adjacent particle.

Nope.

Nope? If you put yourself in the shoes of any particle of the string
or stone, do you feel that the innermost adjacent particle pulls you
towards the center and don't you feel that the outermost adjacent
particle pulls you to the opposite side?

The adjacent particle on the outside exerts the centripetal force that
constrains the observer to move in a circle...

What you wrote is absurd!

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!

If one is centripetal, the other must be centrifugal, and vice versa.

Luigi.

[Guido Wugi]

Post by Luigi Fortunati
The "apparent" force exists in the accelerated frame but does not exist
in the inertial frame.
For example, in the case of the slingshot, the (apparent) centrifugal
force exists in the rotating frame.
Does this mean that (in the rotating reference) there really is a
centrifugal force acting on the stone or do we imagine that there is
but, in reality, it isn't there at all?
Obviously, in the second case, no one would ever think of asking to
which fundamental force it belongs but, in the first case, if a force
really acts on the stone, we should be able to establish what kind of
force it is.
Well, is the apparent centrifugal force that really acts on the stone
during the rotation and in the rotating reference part of one of the 4
fundamental forces?
[[Mod. note -- No. The apparent centrifugal force is an artifact of
working in non-inertial (in this case rotating) coordinates. -- jt]]

Don't we forget Newton's law here (action=reaction)?
In both positions, the anchor point and the rotating mass, two forces
hold each other in equilibrium.
In the anchor point, the centrifugal force transmitted via the rope is
compensated for at each moment by the ground reaction.
In the rotating mass, it is equally compensated by the ground reaction,
transmitted along the rope.
Even in the rotating system, the "rotating observer" will be aware of
their "free movement" being hindered by a reaction in the rope; and
conclude that this is accounted for by their not belonging to an inertial
system.
Consider being in a rotor: https://en.wikipedia.org/wiki/Rotor_(ride)
Do you imply that people are feeling fictitious forces, when they don't
see "proper" movement?

[Luigi Fortunati]

Post by Guido Wugi
Don't we forget Newton's law here (action=reaction)?

I won't forget it for sure because I wrote about these.

Post by Guido Wugi
In both positions, the anchor point and the rotating mass, two forces
hold each other in equilibrium.
In the anchor point, the centrifugal force transmitted via the rope is
compensated for at each moment by the ground reaction.
In the rotating mass, it is equally compensated by the ground reaction,
transmitted along the rope.

All these compensations are Newton's action and reaction forces.

And they are contact forces between adjacent particles (of the string
and of the stone) and not between the particles and the ground!

See my animation
https://www.geogebra.org/m/kx5kk285

Particle B communicates and exchanges action and reaction forces
(centripetal and centrifugal) with particles A and C, particle C with B
and D, and so on.

Only particle A interacts with the ground, not the others.

Post by Guido Wugi
Even in the rotating system, the "rotating observer" will be aware of
their "free movement" being hindered by a reaction in the rope;

Certain! But he is also aware that he himself is exerting a centrifugal
force on the rope!

Post by Guido Wugi
and conclude that this is accounted for by their not belonging to an
inertial system.
Consider being in a rotor: https://en.wikipedia.org/wiki/Rotor_(ride)
Do you imply that people are feeling fictitious forces, when they don't
see "proper" movement?

Absolutely not, they feel real forces.

They feel the real centripetal force of the wall on them and feel that
they are exerting a real centrifugal force on the wall.

[Tom Roberts]

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
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