When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal force.

But the centrifugal force is ONLY in the rotating reference and not in
the inertial one.

So, how is the centrifugal acceleration of water justified EVEN in the
inertial reference where the centrifugal force is not there?

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On Wednesday, July 13, 2022 at 4:50:42 AM UTC-5, Luigi Fortunati wrote:

When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal force.

But the centrifugal force is ONLY in the rotating reference and not in
the inertial one.

So, how is the centrifugal acceleration of water justified EVEN in the inertial reference where the centrifugal force is not there?

"Centrifugal force" is a fictitious force, it doesn't exist. The only
real force is whatever is causing the object (water molecules in this
case) to follow a curved path. The object is not at rest in any
inertial frame.

Rich L.

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On Wednesday, 13 July 2022 at 11:50:42 UTC+2, Luigi Fortunati wrote:

When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal force.

What matters is not really how we get there, just the steady state is
of interest, by which I mean the water is at rest relative to the bucket.

But the centrifugal force is ONLY in the rotating reference and not in
the inertial one.

There is in fact a corresponding centripetal force in the inertial frame
in which the bucket is rotating, which amounts to a combination of the
pressure forces ultimately sustained by the walls of the bucket, and
of course the gravitational force: hence it's obliquus.

So, how is the centrifugal acceleration of water justified EVEN in the inertial reference where the centrifugal force is not there?

That should be clear now. That said, the point with Newton's bucket
(as I get it) is that, in the reference frame *of the bucket*, where does
the apparent *centrifugal* force come from? Since, by relativity, the situation should be totally equivalent to the universe rotating around
a bucket at rest...

Julio

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Luigi Fortunati <fortunati.luigi@gmail.com> wrote:

When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal force.

But the centrifugal force is ONLY in the rotating reference and not in
the inertial one.

So, how is the centrifugal acceleration of water justified EVEN in the inertial reference where the centrifugal force is not there?

This is either completely trivial,
or one of the great mysteries of physics,
depending on your philosophical inclinations.

I'll recapitulate the history:
1) For Newton all this was completely trivial,
the bucket rotates or not, wrt to his 'absolute space'.
2) Then Ernst Mach came along, who said that 'absolute space'
has no basis in empirical fact.
It is nothing but an unwaranted philosophical abomination
that has no place in physics. (by his philosophy of positivism)

All that matters, according to Mach, is relative motion.
So Mach said that the centrifugal and Coriolis forces
must be asumed to be -caused- by all those 'Ferne Sterne'
rotating around the stationary bucket at enormous speeds.
This is known as a form of "Mach's principle".

Einstein has said that Mach served as his inspiration
for getting started on relativity.
But working things out the Einsteinian way led to a great problem.
For Mach all was fine, because Newtonian gravity,
and hence also his 'Machian forces' propagated at infinite speed.
Finite propagation speed at c spoils it.

So now the mystery: empirically we can derive what is non-rotating
by observing motions in the Solar system to great accuracy.
(or in principle, but not in practice, also with a Foucult pendulum)
A frame without centrifugal and Coriolis doesn't rotate, by definition.

OTOH we can also determine what is, or isn't rotating
by looking at Mach's 'Ferne Sterne'.
(nowadays quasars at bilions of lightyears)

And indeed, those two differently defined frames local vs global,
do not rotate wrt each other,
to one of those ludicrous accuracies hat are the rule nowadays.
(would have to look up, think micro-arcseconds/century)

So there you are. [1]
You can shrug your shoulders, and say:
yes of course, how could it be otherwise?
Or you can say:
this is a deep mystery that needs a physical explanation.

Your choice,

Jan
(who hasn't kept up)

[1] This a veritable 'mer a boire'. There is a huge literature
on various forms of Mach's principle, weak, or strong,
or something else, and on how these should be understood.
Nevertheless, the hard empirical core of it has remained,
despite observable distances growing at least a millionfold.

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Julio Di Egidio alle ore 07:29:41 di gioved=EC 14/07/2022 ha scritto:

There is indeed a corresponding centripetal force in the inertial frame in which the bucket rotates ...

The centripetal force exerted by the walls of the bucket on the water
is already present before the bucket starts to rotate, because it must counteract the centrifugal thrust of the water which, even when
stationary, would be set in motion centrifugally outwards if the walls
of the bucket did not oppose.

All of this continues to be there even when the bucket starts spinning
and the water still doesn't.

This ratio between the centrifugal and centripetal forces changes when
even the water starts to spin!

And what happens in this case? Is it the water accelerating
(centrifugally) outward or is the bucket walls accelerating
(centripetally) inward?

Is it the centrifugal force that pushes the water to accumulate against
the walls of the bucket or is it the centripetal force that pushes the
walls of the bucket to tighten against the water?

[[Mod. note -- It appears that you're confusing two quite different
forces:
(a) The outward force the water exerts on the walls of the bucket, and
the corresponding Newton's-3rd-law inward force the walls of the
bucket exert on the water, due to the water's *weight* and Pascal's
law:
... this force is described in
https://en.wikipedia.org/wiki/Vertical_pressure_variation
https://en.wikipedia.org/wiki/Pascal%27s_law
... this force is ONLY present if there's an ambient (vertical)
gravitational field (or an equivalent vertical acceleration);
this force is proportional to the vertical Newtonian "little g"
and is ABSENT if the bucket is in free-fall ("weightless"),
e.g., in a space station
... this force varies with vertical position along the bucket's
walls, i.e., this force goes to zero at the water surface,
and is at a maximum at the bottom of the bucket
... for a given volume/shape filled with water, this force is
INDEPENDENT of the water's spin (or the bucket's spin), so
it's "just" an irrelevant distraction in the context of Newton's
bucket
(b) The outward force the water exerts on the walls of the bucket, and
the corresponding Newton's-3rd-law inward force the walls of the
bucket exert on the water, due to the water's *mass* moving on
an accelerated (spinning) trajectory:
... this force depends on the water's spin (NOT the bucket's spin);
this force is ONLY present if the water is spinning; this force
is ABSENT if the water is not spinning
... this force is INDEPENDENT of vertical position along the bucket's
walls: this force is IDENTICAL at the water surface and at the
bottom of the bucket
... for a given volume/shape filled with water, this force is
INDEPENDENT of the ambient gravitational field (or equivalent
vertical acceleration); notably, this force would be IDENTICAL
if the bucket were in free-fall ("weightless"), e.g., in a
space station
... this force is the one we usually discuss in the context of
Newton's bucket

Now to your specific statements & questions:

The centripetal force exerted by the walls of the bucket on the water
is already present before the bucket starts to rotate, because it must counteract the centrifugal thrust of the water which, even when
stationary, would be set in motion centrifugally outwards if the walls
of the bucket did not oppose.

You're referring to (a) here, which (since it doesn't vary with the water's spin) is not relevant to a discussion of Newton's bucket.

All of this continues to be there even when the bucket starts spinning
and the water still doesn't.

The bucket's spin doesn't matter (for the dynamics of the water); only
the water's spin matters. [The bucket's spin does matter for calculating
the mechanical stresses on the bucket itself, due to the bucket's own
mass moving on an accelerated (spinning) trajectory.]

This ratio between the centrifugal and centripetal forces changes when
even the water starts to spin!

Yes, the statement "the water is spinning" implies the statement that
"the water is accelerated inwards (with respect to an inertial reference frame)" and hence (by Newton's 2nd law) there must be net inwards forces
acting on the water. Those forces are the ones I described in (b) above.

And what happens in this case? Is it the water accelerating
(centrifugally) outward or is the bucket walls accelerating
(centripetally) inward?

For simplicity let's focus on what happens once the bucket has been
spinning at a constant angular velocity for a long time, so that the water
is in uniform rotation at that same angular velocity. [I.e., let's ignore
the transient "startup" phase where the water's rotation is not yet uniform, since the motion then is very complicated and hard to analyze.]

Then the answer to your first question is "no, the water is not accelerating outward with respect to an inertial reference frame", and the answer to your second question is "yes, the bucket walls (and the water) are accelerating inward with respect to an inertial reference frame".
-- jt]]

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In a moderator's note earlier in this thread, I referred to

(b) The outward force the water exerts on the walls of the bucket, and
the corresponding Newton's-3rd-law inward force the walls of the
bucket exert on the water, due to the water's *mass* moving on
an accelerated (spinning) trajectory:

Oops, I made two mistakes there and in the following text.

First, my text above suggests the wrong causality. What I should have
written was/is more like this:

(b) The inward force the walls of the bucket must exert on the water
in order to (by virtue of Newton's 2nd law) cause the water to
move along an accelerated trajectory; by Newton's 3rd law the
water exerts an equal and opposite (outward) force on the walls
of the bucket.

I then went on to write (something which was ok):

... this force depends on the water's spin (NOT the bucket's spin);
this force is ONLY present if the water is spinning; this force
is ABSENT if the water is not spinning

But then I wrote:

... this force is INDEPENDENT of vertical position along the bucket's
walls: this force is IDENTICAL at the water surface and at the
bottom of the bucket

Oops, on further thought I don't think that last statement is true.

It *is* true if the bucket has a tight-fitting (flat) lid so that the
water is constrained to be in a cylindrical shape and to stay in that
shape even when the water is rotating.

But in the more common case where the bucket has an open top and is in
am ambient gravitational field with the Newtonian "little g" pointing
down (so that the water surface forms a concave parabolic surface when
the water is rotating), then I think the force (b) does in fact vary
with vertical position along the bucket's walls. To see this, consider
the following crude ASCII-art diagram (best viewed in a monopitch font)
showing a side view of some uniformly-rotating water in the bucket,
where I've labelled various parts of the water with letters/numbers
denoting their distance from the spin axis:

:
| : |
z=9 |B : B|
z=8 |BA : AB|
z=7 |BA98 : 89AB|
z=6 |BA98765 : 56789AB|
z=5 |BA987654321:123456789AB|
z=4 |BA987654321:123456789AB|
z=3 |BA987654321:123456789AB|
z=2 |BA987654321:123456789AB|
z=1 |BA987654321:123456789AB|
z=0 +-----------:-----------+
:

In the top layer of water (z=9), only the fluid labelled "B" is present
and so the force (b) I described above is only that necessary to accelerate
the water "B".

But in any of the "complete" layers of water (vertical positions z=1
through z=5 inclusive), the force (b) I described above has to accelerate
the larger mass of fluid "1", "2", ..., "B".

This argues that the inwards force (b) I described above is larger in
the z=1 through z=5 vertical positions than it is in the z=9 layer vertical position.

Working out the precise variation of the force with vertical position
is left as an exercise for the reader.

--
-- "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com>
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
currently on the west coast of Canada
"The question of whether machines can think is about as relevant
as the question of whether submarines can swim." - Edsger Dijkstra

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Luigi Fortunati alle ore 11:57:05 di giovedì 14/07/2022 ha scritto:

[[Mod. note

And what happens in this case? Is it the water accelerating
(centrifugally) outward or is the bucket walls accelerating
(centripetally) inward?

For simplicity let's focus on what happens once the bucket has been
spinning at a constant angular velocity for a long time, so that the water
is in uniform rotation at that same angular velocity. [I.e., let's ignore the transient "startup" phase where the water's rotation is not yet uniform, since the motion then is very complicated and hard to analyze.]
-- jt]]

Why do you say that the motion of the transitional phase is very
complicated and hard to analyze? Where do you see all this difficulty?

In this phase, one can easily observe the water which, initially in equilibrium, progressively begins to accelerate towards the outside,
where it ends up accumulating against the walls of the bucket.

If the water accelerates outward, it means that there is a force
directed outward.

If the walls of the bucket do not accelerate inwards, it means that
there are no forces accelerating the walls of the bucket inwards.

It is the water that is set in motion by pushing towards the outside,
not the walls of the bucket which (remaining still) simply block that centrifugal thrust!

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In a moderator's note earlier in this thread, I referred to

(b) The outward force the water exerts on the walls of the bucket, and
the corresponding Newton's-3rd-law inward force the walls of the
bucket exert on the water, due to the water's *mass* moving on
an accelerated (spinning) trajectory:

Oops, I made two mistakes there and in the following text.

First, my text above suggests the wrong causality. What I should have
written was/is more like this:

(b) The inward force the walls of the bucket must exert on the water
in order to (by virtue of Newton's 2nd law) cause the water to
move along an accelerated trajectory; by Newton's 3rd law the
water exerts an equal and opposite (outward) force on the walls
of the bucket.

I then went on to write (something which was ok):

... this force depends on the water's spin (NOT the bucket's spin);
this force is ONLY present if the water is spinning; this force
is ABSENT if the water is not spinning

But then I wrote:

... this force is INDEPENDENT of vertical position along the bucket's
walls: this force is IDENTICAL at the water surface and at the
bottom of the bucket

Oops, on further thought I don't think that last statement is true.

It *is* true if the bucket has a tight-fitting (flat) lid so that the
water is constrained to be in a cylindrical shape and to stay in that
shape even when the water is rotating.

But in the more common case where the bucket has an open top and is in
am ambient gravitational field with the Newtonian "little g" pointing
down (so that the water surface forms a concave parabolic surface when
the water is rotating), then I think the force (b) does in fact vary
with vertical position along the bucket's walls. To see this, consider
the following crude ASCII-art diagram (best viewed in a monopitch font)
showing a side view of some uniformly-rotating water in the bucket,
where I've labelled various parts of the water with letters/numbers
denoting their distance from the spin axis:

:
| : |
z=9 |B : B|
z=8 |BA : AB|
z=7 |BA98 : 89AB|
z=6 |BA98765 : 56789AB|
z=5 |BA987654321:123456789AB|
z=4 |BA987654321:123456789AB|
z=3 |BA987654321:123456789AB|
z=2 |BA987654321:123456789AB|
z=1 |BA987654321:123456789AB|
z=0 +-----------:-----------+
:

In the top layer of water (z=9), only the fluid labelled "B" is present
and so the force (b) I described above is only that necessary to accelerate
the water "B".

But in any of the "complete" layers of water (vertical positions z=1
through z=5 inclusive), the force (b) I described above has to accelerate
the larger mass of fluid "1", "2", ..., "B".

This argues that the inwards force (b) I described above is larger in
the z=1 through z=5 vertical positions than it is in the z=9 layer vertical position.

Working out the precise variation of the force with vertical position
is left as an exercise for the reader.

--
-- "Jonathan Thornburg [remove -color to reply]" <dr.j.thornburg@gmail-pink.com>
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
currently on the west coast of Canada
"The question of whether machines can think is about as relevant
as the question of whether submarines can swim." - Edsger Dijkstra

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On Friday, 15 July 2022 at 01:57:10 UTC+2, Luigi Fortunati wrote:

Julio Di Egidio alle ore 07:29:41 di gioved=EC 14/07/2022 ha scritto:

There is indeed a corresponding centripetal force in the inertial frame in which the bucket rotates ...

The centripetal force exerted by the walls of the bucket on the water
is already present before the bucket starts to rotate, because it must counteract the centrifugal thrust of the water which, even when
stationary, would be set in motion centrifugally outwards if the walls
of the bucket did not oppose.

But that is not "Newton's bucket", it's just something else. Moreover,
and more basically, centripetal/centrifugal is not just any old force,
in fact has not even to do with shapes and "containers", it is
specifically how we call forces that derive from *rotational motion*.

<snip>

This ratio between the centrifugal and centripetal forces changes when
even the water starts to spin!

That just cannot be: those two forces are just two different descriptions
of the same physics, typically associated with the two distinct frames
of reference, the one inertial in which the thing (bucket, spinning top, whatever) is rotating, and the one rotating with the thing.

In fact, more concretely, whichever the frame of reference we
choose, we can draw vectors representing both the centripetal and
the centrifugal force (as measured in their respective frames) and
those two vectors, unless I am badly mistaken, stay identically
equal and opposite.

Incidentally, this is not Newton's third law, though it looks analogous
since it's another case of equal and opposite: the two forces in the
third law actually both exist, are not simply two sides (descriptions)
of the same coin...

Is it the centrifugal force that pushes the water to accumulate against
the walls of the bucket or is it the centripetal force that pushes the
walls of the bucket to tighten against the water?

[[Mod. note -- It appears that you're confusing two quite different
forces:

While I second what the moderator goes on explaining there,
I think that more basic and to the point here was to note that centrifugal/centripetal are, as said, just two sides of the same
one coin.

Julio

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(This entire discussion is in the context of Newtonian mechanics.)

On 7/15/22 9:44 AM, Luigi Fortunati wrote:

If the water accelerates outward, it means that there is a force
directed outward.

In the rotating-bucket coordinates:
As the bucket starts spinning you are correct -- the increasing
"centrifugal force" induces an increasing pressure gradient that causes
the fluid to increasingly rise higher for increasing radius. In a steady
state there is no acceleration anywhere and the net force is zero on
each small portion of the water -- the "centrifugal force" exactly
balances the horizontal fluid force induced by gravity and the
surrounding fluid; the radial pressure gradient causes the surface to be
higher for increasing radius.

In the inertial frame in which the bucket axis is at rest:
As the bucket starts spinning the acceleration of each small portion of
water is rather complicated (nonzero radial and tangential components).
In a steady state there is a centripetal force (directed radially
inward) that is different for each small portion of the water -- this
maintains each portion's "orbit" around the axis. For small portions of
the water against the wall it comes from the wall; for other portions it
comes from neighboring portions of the water. All other components of
force sum to zero for each small portion of the water; the radial
pressure gradient causes the surface to be higher for increasing radius.

If the walls of the bucket do not accelerate inwards, it means that
there are no forces accelerating the walls of the bucket inwards.

In the rotating-bucket coordinates:
in the steady state, the centripetal force on each small portion of the
wall equals the "centrifugal force" on it. All components of force sum
to zero for each small portion of the water. The centripetal force of
the wall is canceled by the "centrifugal force" on it. No portion of
bucket or water accelerates in any direction.

In the inertial frame in which the bucket axis is at rest:
in the steady state, the centripetal force on each small portion of the
wall accelerates it radially inward, maintaining its "orbit" around the
axis. Ditto for the wall. There is, of course, no "centrifugal force".

You should see from the above discussion that it is ESSENTIAL that you
specify which coordinates or frame you are discussing. Your repeated
failure to do that turns what you say into nonsense.

Tom Roberts

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On 7/15/22 6:11 PM, Julio Di Egidio wrote:

I think that more basic and to the point here was to note that centrifugal/centripetal are, as said, just two sides of the same one
coin.

Not at all! They are VERY different: centripetal force is a real force,
usually one that keeps one object in orbit around another object;
"centrifugal force" is a fictitious "force" used in Newtonian mechanics
to permit one to act as if rotating coordinates were inertial, so one
can apply Newton's laws -- in general that is not sufficient and one
also needs "Coriolis and Euler forces" (which are also fictitious).

[I put fictitious "forces" in scare quotes, because
they are not really forces.]

The difference is: a real force cannot be made to vanish by changing coordinates, while a fictitious "force" will vanish in inertial
coordinates. As nature uses no coordinates, all natural phenomena must
be independent of coordinates; contrariwise, all coordinate-dependent quantities are purely human inventions. Note this distinction is theory dependent: in Newtonian mechanics the force of gravity is real, while in General Relativity it is fictitious.

Ultimately all fictitious "forces" can be traced to geometry: in GR they
are directly related to specific components of the connection.

Tom Roberts

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Tom Roberts alle ore 11:11:21 di venerdì 15/07/2022 ha scritto:

You should see from the above discussion that it is ESSENTIAL that you specify which coordinates or frame you are discussing. Your repeated
failure to do that turns what you say into nonsense.

None of the things I said happen in one reference yes and in the other
no.

The accumulation of water on the walls of the bucket occurs in ALL
references.

The transition from initially still water particles and then moving
outwards (radial acceleration) occurs in ALL references.

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On Sunday, 17 July 2022 at 22:04:06 UTC+2, Tom Roberts wrote:

On 7/15/22 6:11 PM, Julio Di Egidio wrote:

I think that more basic and to the point here was to note that centrifugal/centripetal are, as said, just two sides of the same one
coin.

Not at all! They are VERY different: centripetal force is a real force, usually one that keeps one object in orbit around another object; "centrifugal force" is a fictitious "force" used in Newtonian mechanics
to permit one to act as if rotating coordinates were inertial, so one

No, "apparent" is indeed a technical term referring specifically to the fact that the description in the inertial frame is the privileged one, the one for which the laws of mechanics hold: but that doesn't mean that if you hop
on a merry-go-round you mustn't hold yourself to prevent falling off...

So, the two sides, i.e. descriptions, of the same one coin: and then one
should also note that too much emphasis on just inertial frames and
motion is also and in itself an aberration...

Julio

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Tom Roberts alle ore 07:54:37 di domenica 17/07/2022 ha scritto:

The difference is: a real force cannot be made to vanish by changing coordinates, while a fictitious "force" will vanish in inertial
coordinates.

Exactly.

I totally agree with you, the fictitious force disappears in the inertial reference.

But if it doesn't go away, obviously it's not fictitious!

So, look at my animation
https://www.geogebra.org/m/mrthyefq

We are in an inertial reference where the centrifugal force should not be there.

Still, the rope gets longer!

Can you explain to me how it stretches if there is no centrifugal force?

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On 7/18/22 4:50 AM, Luigi Fortunati wrote:

Tom Roberts alle ore 07:54:37 di domenica 17/07/2022 ha scritto:

The difference is: a real force cannot be made to vanish by
changing coordinates, while a fictitious "force" will vanish in
inertial coordinates.

I totally agree with you, the fictitious force disappears in the
inertial reference. But if it doesn't go away, obviously it's not
fictitious!

In inertial coordinates, "fictitious forces" DO go away, as you agreed.

So, look at my animation https://www.geogebra.org/m/mrthyefq We are
in an inertial reference where the centrifugal force should not be
there. Still, the rope gets longer!

Yes.

Can you explain to me how it stretches if there is no centrifugal
force?

To start the object going around in the circle, you had to give the
object an impulse [#] to the right; your drawing also starts the object
at the (pre-computed) radius with which it will orbit [@]. To keep the
object orbiting in a circle, the rope must pull it off its inertial straight-line path -- that pull is the centripetal force that keeps the
object in circular orbit, and is what stretches the rope. No
"centrifugal force" is involved.

[#] Large force of very short duration.
[@] Given the elasticity of the rope. There is an initial
radially-outward force on the object to stretch the rope
appropriately; it vanishes as soon as the object starts
to move, as the rope then provides the centripetal force.
This initial outward force, the initial position of the
object, and the magnitude of the initial impulse, must
all be coordinated to make the object's path a circle.

Tom Roberts

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Jonathan Thornburg [remove -color to reply] <dr.j.thornburg@gmail-pink.com> wrote:

[ASCII parabola]

But in any of the "complete" layers of water (vertical positions z=1 a through z=5 inclusive), the force (b) I described above has to accelerate
the larger mass of fluid "1", "2", ..., "B".

This argues that the inwards force (b) I described above is larger in
the z=1 through z=5 vertical positions than it is in the z=9 layer vertical position.

Working out the precise variation of the force with vertical position
is left as an exercise for the reader.

Which is again made trivial by noting that the centrifugal force can be
derived from the centrifugal potential. The parabolic shape is an
equipotential surface, [1] when everything is stationary in co-rotating coordinates,

Jan

[1] So the surface is given by g z = 1/2 \Omega^2 (x^2 + y^2) if the
origin is chosen suitably.

[added] So the centrifugal `force' is not just a force that acts
somewhere, it is actually a force field. It appears as such in for
example meteorological models, which are of course done on a rotating
Earth. (but Coriolis is more important)

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Luigi Fortunati <fortunati.luigi@gmail.com> wrote:

Tom Roberts alle ore 11:11:21 di venerdì 15/07/2022 ha scritto:

You should see from the above discussion that it is ESSENTIAL that you specify which coordinates or frame you are discussing. Your repeated failure to do that turns what you say into nonsense.

None of the things I said happen in one reference yes and in the other
no.

The accumulation of water on the walls of the bucket occurs in ALL references.

The transition from initially still water particles and then moving
outwards (radial acceleration) occurs in ALL references.

Phillip Helbig <helbig@star.herts.ac.uk> wrote:

[-]

But in the more common case where the bucket has an open top and is in
am ambient gravitational field with the Newtonian "little g" pointing
down (so that the water surface forms a concave parabolic surface when
the water is rotating), then I think the force (b) does in fact vary
with vertical position along the bucket's walls. To see this, consider
the following crude ASCII-art diagram (best viewed in a monopitch font) showing a side view of some uniformly-rotating water in the bucket,
where I've labelled various parts of the water with letters/numbers
denoting their distance from the spin axis:

:
| : |
z=9 |B : B|
z=8 |BA : AB|
z=7 |BA98 : 89AB|
z=6 |BA98765 : 56789AB|
z=5 |BA987654321:123456789AB|
z=4 |BA987654321:123456789AB|
z=3 |BA987654321:123456789AB|
z=2 |BA987654321:123456789AB|
z=1 |BA987654321:123456789AB|
z=0 +-----------:-----------+
:

In the top layer of water (z=9), only the fluid labelled "B" is present
and so the force (b) I described above is only that necessary to accelerate the water "B".

But in any of the "complete" layers of water (vertical positions z=1
through z=5 inclusive), the force (b) I described above has to accelerate
the larger mass of fluid "1", "2", ..., "B".

This argues that the inwards force (b) I described above is larger in
the z=1 through z=5 vertical positions than it is in the z=9 layer vertical position.

Working out the precise variation of the force with vertical position
is left as an exercise for the reader.

Which is again made trivial by noting that the centrifugal force
can be derived from the centrifugal potential.
The parabolic shape is an equipotential surface, [1]
when everything is stationary in co-rotating coordinates,

Jan

[1] So the surface is given by g z = 1/2 \Omega^2 (x^2 + y^2)
if the origin is chosen suitably.

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Tom Roberts alle ore 07:14:21 di lunedì 18/07/2022 ha scritto:

On 7/18/22 4:50 AM, Luigi Fortunati wrote:

Tom Roberts alle ore 07:54:37 di domenica 17/07/2022 ha scritto:

The difference is: a real force cannot be made to vanish by
changing coordinates, while a fictitious "force" will vanish in
inertial coordinates.

I totally agree with you, the fictitious force disappears in the
inertial reference. But if it doesn't go away, obviously it's not
fictitious!

In inertial coordinates, "fictitious forces" DO go away, as you agreed.

So, look at my animation https://www.geogebra.org/m/mrthyefq We are
in an inertial reference where the centrifugal force should not be
there. Still, the rope gets longer!

Yes.

Can you explain to me how it stretches if there is no centrifugal
force?

To start the object going around in the circle, you had to give the
object an impulse [#] to the right; your drawing also starts the object
at the (pre-computed) radius with which it will orbit [@]. To keep the
object orbiting in a circle, the rope must pull it off its inertial straight-line path -- that pull is the centripetal force that keeps the object in circular orbit, and is what stretches the rope. No
"centrifugal force" is involved.

[#] Large force of very short duration.
[@] Given the elasticity of the rope. There is an initial
radially-outward force on the object to stretch the rope
appropriately; it vanishes as soon as the object starts
to move, as the rope then provides the centripetal force.

It is true that the rope provides its centripetal force to the object B
of my animation
https://www.geogebra.org/m/mrthyefq
but it is also true that, at the same time, object B provides the rope
with centrifugal force, otherwise the rope could not maintain its
elongation over time (elongation present in all references).

Centripetal and centrifugal forces act together and never separately:
one exists only by virtue of the fact that the other also exists (and
vice versa).

The centripetal force of A on B could not exist without the
corresponding (and opposite) centrifugal force of B on A.

Therefore the centrifugal force of A on B cannot disappear until the centripetal force of B on A also disappears.

Luigi Fortunati

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Luigi Fortunati <fortunati.luigi@gmail.com> wrote:

Tom Roberts alle ore 07:14:21 di lunedì 18/07/2022 ha scritto:

On 7/18/22 4:50 AM, Luigi Fortunati wrote:

Tom Roberts alle ore 07:54:37 di domenica 17/07/2022 ha scritto:

The difference is: a real force cannot be made to vanish by
changing coordinates, while a fictitious "force" will vanish in
inertial coordinates.

I totally agree with you, the fictitious force disappears in the
inertial reference. But if it doesn't go away, obviously it's not
fictitious!

In inertial coordinates, "fictitious forces" DO go away, as you agreed.

So, look at my animation https://www.geogebra.org/m/mrthyefq We are
in an inertial reference where the centrifugal force should not be
there. Still, the rope gets longer!

Yes.

Can you explain to me how it stretches if there is no centrifugal
force?

To start the object going around in the circle, you had to give the
object an impulse [#] to the right; your drawing also starts the object
at the (pre-computed) radius with which it will orbit [@]. To keep the object orbiting in a circle, the rope must pull it off its inertial straight-line path -- that pull is the centripetal force that keeps the object in circular orbit, and is what stretches the rope. No
"centrifugal force" is involved.

[#] Large force of very short duration.
[@] Given the elasticity of the rope. There is an initial
radially-outward force on the object to stretch the rope
appropriately; it vanishes as soon as the object starts
to move, as the rope then provides the centripetal force.

It is true that the rope provides its centripetal force to the object B
of my animation
https://www.geogebra.org/m/mrthyefq
but it is also true that, at the same time, object B provides the rope
with centrifugal force, otherwise the rope could not maintain its
elongation over time (elongation present in all references).

Centripetal and centrifugal forces act together and never separately:
one exists only by virtue of the fact that the other also exists (and
vice versa).

The centripetal force of A on B could not exist without the
corresponding (and opposite) centrifugal force of B on A.

Therefore the centrifugal force of A on B cannot disappear until the centripetal force of B on A also disappears.

It seems to me that your problems are caused
by the use of non-standard terminology,
such as calling the reaction to the centripetal force
a centrifugal force.
'Centrifugal force' has a welll defined technical meaning,
(as the pseudo-force in rotating coordinates)
and you shouldn't use the term for anything else.
(like a force the happens to point towards the centre)

Perhaps the method employed by my high school teacher,
long ago, can help you.
At the start of dealing with the subject he declared:
---- CENTRIFUGAL FORCES DO NO EXIST ----
and any pupil who dared to mention the word
got A BIG FAT RED CROSS through his work.
(so no talk about rotating coordinates)

He correctly saw that mixing centrifugal force from rotating coordinates
with centripetal force from stationary coordinates can only end
with pupils getting thoroughly confused.
(like thinking that the two can, or sould balance each other)

So a BIG FAT RED CROSS for you, for what you wrote above,

Jan

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J. J. Lodder alle ore 13:32:02 di mercoledì 20/07/2022 ha scritto:

...
Perhaps the method employed by my high school teacher,
long ago, can help you.
At the start of dealing with the subject he declared:
---- CENTRIFUGAL FORCES DO NO EXIST ----

It is undoubtedly true that there are centrifugal forces ("apparent" or "fictitious") that do not exist.

There is, for example, the force that (in the driver's eyes) accelerates the lighter on the dashboard of the car when cornering.

This acceleration is truly fictitious because it disappears in the inertial reference and does not stretch any elastic cord.

But the case with my animation
https://www.geogebra.org/m/mrthyefq
it is completely different because the elastic cord that stretches is there.

So how could the elastic cord stretch (in all references) if (in this specific case) there is no centrifugal force?

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Am 21.07.2022 um 13:17 schrieb Luigi Fortunati:

J. J. Lodder alle ore 13:32:02 di mercoledì 20/07/2022 ha scritto:

...
Perhaps the method employed by my high school teacher,
long ago, can help you.
At the start of dealing with the subject he declared:
---- CENTRIFUGAL FORCES DO NO EXIST ----

It is undoubtedly true that there are centrifugal forces ("apparent"
or "fictitious") that do not exist.

There is, for example, the force that (in the driver's eyes)
accelerates the lighter on the dashboard of the car when cornering.

This acceleration is truly fictitious because it disappears in the
inertial reference and does not stretch any elastic cord.

But the case with my animation
https://www.geogebra.org/m/mrthyefq
it is completely different because the elastic cord that stretches is there.

So how could the elastic cord stretch (in all references) if (in this specific case) there is no centrifugal force?

It is simply (for your understanding level) your force, that
accellerates your ball on the cord keeping it on a circular path. If you
don't keep the rope fixed in the origine and nobody accelerates your
ball, then nothing is stretched.

So in the end, you are stretching the rope.

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Luigi Fortunati <fortunati.luigi@gmail.com> wrote:

J. J. Lodder alle ore 13:32:02 di mercoledà 20/07/2022 ha scritto:

...
Perhaps the method employed by my high school teacher,
long ago, can help you.
At the start of dealing with the subject he declared:
---- CENTRIFUGAL FORCES DO NO EXIST ----

It is undoubtedly true that there are centrifugal forces ("apparent" or "fictitious") that do not exist.

There is, for example, the force that (in the driver's eyes) accelerates
the lighter on the dashboard of the car when cornering.

This acceleration is truly fictitious because it disappears in the
inertial reference and does not stretch any elastic cord.

But the case with my animation https://www.geogebra.org/m/mrthyefq it is completely different because the elastic cord that stretches is there.

So how could the elastic cord stretch (in all references) if (in this specific case) there is no centrifugal force?

Again, you confuse yourself with your incorrect terminology.
The term 'centrifugal force' has a well defined technical meaning.
It is the universal apparent force that appears
in a rotating coordinate system, acting on any mass element,
and equal to dm grad (-1/2 \Omega^2 (x^2 + y^2)
Nothing else should be called a 'centrifugal force'.
(on pain of a BIG FAT RED CROSS through your work)

So by definition no 'centrifugal force' can exist
in a non-rotating coordinate system.

If there are forces pointing out
from what can be taken as a rotation axis
they are NOT centrifugal forces.
Calling them that is just a beginner's error,

Jan
(who doesn't look at animations)

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On 7/20/22 1:39 AM, Luigi Fortunati wrote:

It is true that the rope provides its centripetal force to the
object B of my animation https://www.geogebra.org/m/mrthyefq but it
is also true that, at the same time, object B provides the rope with
centrifugal force, otherwise the rope could not maintain its
elongation over time (elongation present in all references).

That is NOT "centrifugal force". That is merely the usual force of
tension in the rope.

If you simply pull on a rope connected to a mass, in a straight line, no rotation, your pull will induce tension in the rope, and the tension
force will accelerate the mass. We don't usually discuss the "force the
mass exerts on the rope", but if we did it would merely be the reaction
force of Newton's 3rd law (responding to the force of tension the rope
exerts on the mass).

As Jan has pointed out, you confuse yourself, and your readers, by using
the term "centrifugal force" for situations in which it simply does not
exist. While there can be other "center-fleeing forces", "centrifugal
force" is a technical term with a specific meaning that applies ONLY in rotating coordinates.

Tom Roberts

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Torn Rumero DeBrak alle ore 15:59:04 di giovedì 21/07/2022 ha scritto:

But the case with my animation
https://www.geogebra.org/m/mrthyefq
it is completely different because the elastic cord that stretches is there. >>
So how could the elastic cord stretch (in all references) if (in this
specific case) there is no centrifugal force?

It is simply (for your understanding level) your force, that
accellerates your ball on the cord keeping it on a circular path.

A single force is not enough to stretch an elastic cord, you need two of opposite sign.

But let's see how the forces work in this case.

The centripetal force of my hand acts on one end of the bungee cord and
the centrifugal force of the end of the bungee cord acts on my hand.

They are two opposing forces and not just one.

The centripetal force of the other end of the cord acts on the ball and
the centrifugal force of the ball acts on the other end of the string.

Again, the forces act in pairs and not alone.

There is no point on the hand, cord and ball where there is the action
of a single force without the reaction of the opposite one.

So in the end, you are stretching the rope.

Yes, I am stretching the rope (pulling it to one side) but on the other
side there is the ball is pulling it from the opposite side!

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[Moderator's note: It seems that all has been said which can be
meaningfully said in this thread. Thus, any future posts must present something truly new rather than just a repeat (rephrased or not) of
previous exchanges. -P.H.]

Luigi Fortunati <fortunati.luigi@gmail.com> wrote:

Torn Rumero DeBrak alle ore 15:59:04 di giovedà 21/07/2022 ha scritto:

But the case with my animation
https://www.geogebra.org/m/mrthyefq
it is completely different because the elastic cord that stretches is >>there.

So how could the elastic cord stretch (in all references) if (in this
specific case) there is no centrifugal force?

It is simply (for your understanding level) your force, that
accellerates your ball on the cord keeping it on a circular path.

A single force is not enough to stretch an elastic cord, you need two of opposite sign.

YES.

But let's see how the forces work in this case.

The centripetal force of my hand acts on one end of the bungee cor

YES.

and the centrifugal force of the end of the bungee cord acts on my hand.

BIG FAT RED CROSS.

They are two opposing forces and not just one.

BIG FAT RED CROSS.

The centripetal force of the other end of the cord acts on the ball and

YES.

the centrifugal force of the ball acts on the other end of the string.

BIG FAT RED CROSS.

Again, the forces act in pairs and not alone.

Just action = reaction, otherwise
there could be no momentum conservation.

There is no point on the hand, cord and ball where there is the action
of a single force without the reaction of the opposite one.

Sure, third law always holds.

So in the end, you are stretching the rope.

Yes, I am stretching the rope (pulling it to one side) but on the other
side there is the ball is pulling it from the opposite side!

YES.
The forces on the ball are not balanced,
hence it accelerates all the time.
At the attachement point the forces do balance.
(force of rope on ball equals force of ball on rope)

It is an error to call that reaction force 'a centrifugal force'.
THERE ARE NO CENTRIFUGAL FORCES.
(high school teacher, again)

Jan

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On Friday, 22 July 2022 at 13:04:58 UTC+2, J. J. Lodder wrote:

[Moderator's note: It seems that all has been said which can be
meaningfully said in this thread. Thus, any future posts must present something truly new rather than just a repeat (rephrased or not) of
previous exchanges. -P.H.]

But no agreement has been reached even among those posting
answers, indeed here I feel compelled to try and again object/
question:

Luigi Fortunati <fortuna...@gmail.com> wrote:

Torn Rumero DeBrak alle ore 15:59:04 di giovedà 21/07/2022 ha scritto: <snip>

It is an error to call that reaction force 'a centrifugal force'.
THERE ARE NO CENTRIFUGAL FORCES.

I'd say that is indeed an error, but not for that reason:

If you hop on a merry go round and don't hold yourself...
and then I won't repeat what I have said upthread, but if we
actually *measure* the acceleration locally, we do find that
there is in a force, a very concrete one: so, to say that
centrifugal forces plain "do not exist" is simply wrong and
eventually misleading.

In fact, here is my own summary of the scenarios here:

In the inertial frame in which -say- a ball is attached to and
rotating around a central pivot at rest, there is a *centripetal*
force from the ball directed to the center (at every instant),
and the reaction is the contrary force pulling the central
pivot towards the ball.

OTOH, in the rotating frame in which the ball is at rest, there
is a *centrifugal* force pulling the ball *away from* the central
pivot, and the reaction is again the contrary force at the central
pivot, i.e. here *away from* the ball. So, indeed the analogous
to the inertial description, but in opposite directions: outwards
instead of inwards.

And now, just to be clear, back to errors and reasons: it is not
that centrifugal/centripetal are related by Newton's third law
(the error): rather, they exist in distinct frames of reference,
and each sees a corresponding reaction as per the third law
(the reason).

No?

Julio

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On 7/22/22 12:39 PM, Julio Di Egidio wrote:

centrifugal/centripetal [forces] exist in distinct frames of reference,

It is quite clear that nature uses no frames of reference or
coordinates, so every natural phenomenon MUST be independent of frame or coordinates -- they are purely human constructs we use to DESCRIBE what happens. So "centrifugal force" cannot possibly be real (a natural
phenomenon).

If you hop on a merry go round and don't hold yourself...
if we
actually *measure* the acceleration locally, we do find that
there is in a force, a very concrete one: so, to say that
centrifugal forces plain "do not exist" is simply wrong and
eventually misleading.

You didn't completely describe what you are discussing (your "locally"
is undefined). This is only "misleading" to people who ignore the
context and use incomplete descriptions: Yes, if you measure the
acceleration or force in the rotating coordinates you find a non-zero "centrifugal force". If you measure it in the inertial frame in which
the center is at rest, you find zero force. Now see my previous paragraph.

IOW: saying "centrifugal forces do not exist" is just using the usual
meaning that existence applies to the world, and figments of human
imaginations simply do not exist.

(I agree with the moderator that that all has been said which can be meaningfully said in this thread.)

Tom Roberts

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[Moderator's note: It seems that all has been said which can be
meaningfully said in this thread. Thus, any future posts must present something truly new rather than just a repeat (rephrased or not) of
previous exchanges. -P.H.]

A piece of advice from a physics teacher, translated and somewhat
paraphrased for politeness:

"Shut up and do the math".

The transformation equations to a Newtonian rotating frame are
well known. Just apply them to the problem at hand and study
the results.

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On Saturday, 23 July 2022 at 11:49:19 UTC+2, Tom Roberts wrote:

On 7/22/22 12:39 PM, Julio Di Egidio wrote:

centrifugal/centripetal [forces] exist in distinct frames of reference,

It is quite clear that nature uses no frames of reference or
coordinates, so every natural phenomenon MUST be

Utter nonsense: the physics is the same, the description is not.

independent of frame or
coordinates -- they are purely human constructs we use to DESCRIBE what happens. So "centrifugal force" cannot possibly be real (a natural phenomenon).

If you hop on a merry go round and don't hold yourself...
if we
actually *measure* the acceleration locally, we do find that
there is in a force, a very concrete one: so, to say that
centrifugal forces plain "do not exist" is simply wrong and
eventually misleading.

You didn't completely describe what you are discussing (your "locally"
is undefined). This is only "misleading" to people who ignore the
context and use incomplete descriptions: Yes, if you measure the
acceleration or force in the rotating coordinates you find a non-zero "centrifugal force". If you measure it in the inertial frame in which
the center is at rest, you find zero force.

NO!!, now the other way round: you find that a centripetal force must
exist applied to the ball as the ball is NOT in uniform motion!!

And my "locally" is perfectly defined, the one who is at least confused
and utterly misleading is still you (and co).

IOW: saying "centrifugal forces do not exist" is

...utterly wrong and misleading...

Enough said.

Julio

[Moderator's note: As Julio notes, and as did I in a recent moderator's
note, it does seem that all has been said in this thread; it is making
no more progress, so let's end it. -P.H.]

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In this discussion the following question remained unanswered: "In my animation, and in the rotating reference in which the centrifugal force
exists, who is exercising it, who is undergoing it and what is its point
of application?".

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Luigi Fortunati <fortunati.luigi@gmail.com> wrote:

[one last time]

[Moderator's note: Yes, definitely! -P.H.]

In this discussion the following question remained unanswered: "In my animation, and in the rotating reference in which the centrifugal force exists, who is exercising it,

No one, it is a universal force.

who is undergoing it

Every mass point.

and what is its point of application?".

There is no point of application.
The centrifugal force is a -force field- that acts everywhere,
on every mass element.

And one last time:
You really should find out what the 'centrifugal force' is
according to everybody else, before trying to invent your own.

Jan

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Hi together

"So, how is the centrifugal acceleration of water justified EVEN in the inertial reference where the centrifugal force is not there? "

Simple (first, from the beginning) Question might have no answer.

I thought about it too. (Who not!)
So I had a private answer at least by the aid of Einstein I hope.

1. In reality no (100%) inertial frame of reference does exist.
But this does not answer the question. But helps to understand Mach?

2. If you are a part of Newtons rotating bucket, let us say a water
molecule! You (molecule) do not know: Is there a new gravitational
force acting or are all molecules simply rotating (accelerating by
Newton himself).

3. If you are an observer outside the rotating bucket, standing still on
earth (which does not stand still). You know there is not a new G-Force
acting on molecules, there is a centrifugal force only, which is not
affecting on you like a G-Force could or would but there is acceleration
on the molecules simple to see for you but not for
molecules. Unfortunately you can not tell them what happens. So they
have two unique explanations. One is wrong. They never can find out. Man
can. (Woman of course too)

Best wishes
M.

By the way. Newtons definition of force from the Momentum Equation adopted F=dP/dt=f1+f2+f3+f4+f5
leads to 5 force contributions from pure math applied. (We do not find all in textbooks!)

Now the "physics(nature)" must give them reality (by inventing,
Einsteins wording, f1 up to f5) which nature might follow or not tells
us the experiment. f3 is Coriolis and f5 I don't know. f2 is Mass*Acceleration. We do not have it in textbooks. But every student can
find f1 to f5 by simple product rule applied! If you like see "mano4848 Sommerfeld Fine Structure Constant" (private investigation on YouTube) https://www.youtube.com/results?search_query=manfred+sommerfeld+FSK

--- SoupGate-Win32 v1.05
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[[Mod. note --
1. I apologise for the delay in processing this article, which arrived
in my moderation email on 2022-10-27, but was unfortunately
misclassified as spam by my email provider.
2. I have rewrapped overly-long lines.
-- jt]]

On Wednesday, July 13, 2022 at 5:50:42 AM UTC-4, Luigi Fortunati wrote:

When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal force.

But the centrifugal force is ONLY in the rotating reference and not in
the inertial one.

So, how is the centrifugal acceleration of water justified EVEN in the inertial reference where the centrifugal force is not there?

Centrifugal forces in rotational reference frames are not
active forces but reactive forces. The active force on any given
point of a spinning object is the centripetal force imposed on it
by the mass-points on the same radius ..namely the ONES which are
closer to the rotational axis. The reaction force ,to the centripetal
force exerted in-and-on this given point......is the so called
centrifugal force. Objects.......exterior to the spinning body...will
appear rotating on circles around the same centre ...that is they
appear to be .....one would say..under the effect of some centripetal
forces. That said..... the mandatory force to exist in a rotational
frame is...the centripetal force ..and NOT the centrifugal force !
So...for parts of a spinning solid ,there is an action (centripetal
force)..and accordingly... there is a reaction (centrifugal force).
For matter which is outside of the spinning solid...there is ONLY...a centripetal force, in the reference frame of that given solid.
Best regards, LL

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On 11/1/22 2:44 AM, xray4abc wrote:

Centrifugal forces in rotational reference frames are not active
forces but reactive forces.

No. Here's why:

Consider a mass with a rope attached, and you pull on the rope, straight
away from the mass -- i.e. you apply a force to the rope, which is
clearly an active force. The reactive force of Newton's third law is the tension of the rope, generated by the inertia of the mass and the force
you applied to the rope. To apply Newton's laws, one must use an
inertial frame, and I am implicitly using one when I describe this
physical situation that way.

Now consider the exact same physical situation, but using rotating
coordinates. To be clear, no object is rotating, only the coordinates
are rotating. The active and reactive forces remain exactly the same
(because coordinates are a human construct that cannot possibly affect
any natural/physical phenomenon, such as forces). But if you want to
apply Newton's laws using those rotating coordinates, you must also
include "centrifugal, Coriolis, and Euler forces" -- these are purely
artifacts of using the rotating coordinates. They are not real in any
sense of the word, and they are not "reactive", they are FICTIONS
created by human mathematics in order to permit a human analyst to act
as if Newton's laws applied in the rotating coordinates.

[Note: I put "centrifugal, Coriolis, and Euler forces" in
"scare quotes" because those names are inappropriate and
lead all too many people to error. They are not really
forces, they are imaginary constructs of human minds.
But the names are solidly established historically.]

The active force on any given point of a spinning object is the
centripetal force imposed on it by the mass-points on the same
radius ..namely the ONES which are closer to the rotational axis.
The reaction force ,to the centripetal force exerted in-and-on this
given point......is the so called centrifugal force.

No. The reactive force is the tension on whatever is exerting the
centripetal force on the object, and it is generated by the inertia of
the object and the centripetal force. The "centrifugal force" is purely
an artifact of the mathematics of using rotating coordinates -- mental constructs of humans are not real.

[... repetitions of the above]

Tom Roberts

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Il 02/11/22 09:04, Tom Roberts ha scritto:

On 11/1/22 2:44 AM, xray4abc wrote:

Centrifugal forces in rotational reference frames are not active
forces but reactive forces.

No. Here's why:

.

... "centrifugal, Coriolis, and Euler forces" -- these are purely

artifacts of using the rotating coordinates. They are not real in any
sense of the word, and they are not "reactive", they are FICTIONS
created by human mathematics in order to permit a human analyst to act
as if Newton's laws applied in the rotating coordinates.

[Note: I put "centrifugal, Coriolis, and Euler forces" in
"scare quotes" because those names are inappropriate and
lead all too many people to error. They are not really
forces, they are imaginary constructs of human minds.
But the names are solidly established historically.]

....
The "centrifugal force" is purely

an artifact of the mathematics of using rotating coordinates -- mental constructs of humans are not real.

It is an endless debate about the status of the so-called fictitious (or inertial) forces. Saying that they are "purely artifacts", "not real in
any sense of the word", "imaginary constructs", amd so on, risks to
create at least as many misunderstandings as such statements would like
to avoid.

It is a fact that such "imaginary constructs" are routinely used in
weather forecast, balistic, and other real life activities. It is
pedagogically wrong to convey the idea that such things do not exist.

The key point every consideration about such topics should start with a
clear statement about the definition of force he/she is using.

If we define "force" only the quantity causing acceleration as a
conesquence of the interaction between differen bodies, certainly
"inertial forces" are not forces. If we follow Mach's point of view,
defining force through F-ma, they are. The choice between these two
points of view it is largely matter of taste, provided one sticks to a
well definite conceptual framework.

Whatever is the definition, it is also a fact that at the end of the
day, what really matters is the expression of the acceleration of one
body in terms of all the relevant variables. It is again a fact that,
whatever is the name we give to such espression, newtonian dynamics
allows to maintain the same mathematical structure of second order
ODE's, even if decide to describe the motion in a non-inertial system.

I think this is the really important fact. Decisions about the naming conventions are irrelevant for the formal and numerical results.

To come back to Newton's bucket, the ability of describing what happens
in terms of inertial an non-inertial reference frames is an useful
conceptual exercise, independently of the names assigned to different
formal ingredients.

Giorgio

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On Wednesday, July 13, 2022 at 5:50:42 AM UTC-4, Luigi Fortunati wrote:

When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal force.

But the centrifugal force is ONLY in the rotating reference and not in
the inertial one.

So, how is the centrifugal acceleration of water justified EVEN in the inertial reference where the centrifugal force is not there?

Right!!
In our ,that is exterior, reference frame...we realize that the water is forced into movement by
the friction between itself and the bucket.
The water layers situated close to the walls of the bucket will be the firsts to be
accelerated and then gradually the ones in the central area(by the rotation axis).
The different layers will have different speeds of the flow and according to Bernoulli's Laws from fluid mechanics.....different internal hydrostatic pressure.
The higher the speed of the particles of the layer ..the lower the statical pressure is
(exerted in all directions) in that particular layer.
Then....the statical pressure exerted by the inner layers is higher thant he one exerted by the layers close to the
wall of the bucket. This can explain why the water/liquid rushes from the centre toward the walls.
And this..until the state of equilibrium sets in.
Even school children can easily understand this, after a simple practical demonstration of Bernoulli's
law in air (for example, blowing air by a vertical piece of paper, held by one end by a person).
NO NEED after all, of using reference frames, dubious centrifugal forces etc,! Best regards, Laszlo Lemhenyi

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On 11/3/22 3:39 AM, xray4abc wrote:

On Wednesday, July 13, 2022 at 5:50:42 AM UTC-4, Luigi Fortunati
wrote:

When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal
force.

... only in the rotating-bucket coordinates. In any inertial frame the
water does not "accelerate outwards", it merely tries to move in a
straight line -- in the rotating coordinates that is indeed accelerating outward.

But the centrifugal force is ONLY in the rotating reference and
not in the inertial one.

Right. Ditto for any "centrifugal acceleration".

So, how is the centrifugal acceleration of water justified EVEN in
the inertial reference where the centrifugal force is not there?

It isn't justified, because it does not exist. You seem to be confusing straight-line motion in an inertial frame with "centrifugal acceleration".

In our ,that is exterior, reference frame...we realize that the
water is forced into movement by the friction between itself and
the bucket.

Sure. That accelerates it both tangentially and radially inward.

Tom Roberts

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Tom Roberts lunedì 07/11/2022 alle ore 03:57:05 ha scritto:

On 11/3/22 3:39 AM, xray4abc wrote:

On Wednesday, July 13, 2022 at 5:50:42 AM UTC-4, Luigi Fortunati wrote:

When Newton's bucket starts to rotate, the water slowly starts to rotate as well and accelerates outwards due to the centrifugal force.

... only in the rotating-bucket coordinates. In any inertial frame the water does not "accelerate outwards", it merely tries to move in a
straight line -- in the rotating coordinates that is indeed accelerating outward.

But the centrifugal force is ONLY in the rotating reference and
not in the inertial one.

Right. Ditto for any "centrifugal acceleration".

So, how is the centrifugal acceleration of water justified EVEN in the inertial reference where the centrifugal force is not there?

It isn't justified, because it does not exist. You seem to be confusing straight-line motion in an inertial frame with "centrifugal acceleration".

No, the centripetal acceleration in the inertial reference is there.

Look at my animation
https://www.geogebra.org/m/fpwnumsy

Initially the bucket is stationary and the water does not move: zero speed.

When the rotation begins, the water begins to move from the center outwards (towards the walls of the bucket where it accumulates).

The change in water speed from zero to greater than zero is (like all changes in speed) an acceleration.

Centrifuge, in this case, because it moves radially away from the center to the outside.

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On Monday, November 7, 2022 at 1:57:09 PM UTC-5, Tom Roberts wrote:

On 11/3/22 3:39 AM, xray4abc wrote:

On Wednesday, July 13, 2022 at 5:50:42 AM UTC-4, Luigi Fortunati
wrote:

When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal
force.

... only in the rotating-bucket coordinates. In any inertial frame the
water does not "accelerate outwards", it merely tries to move in a
straight line -- in the rotating coordinates that is indeed accelerating outward.

But the centrifugal force is ONLY in the rotating reference and
not in the inertial one.

Right. Ditto for any "centrifugal acceleration".

So, how is the centrifugal acceleration of water justified EVEN in
the inertial reference where the centrifugal force is not there?

It isn't justified, because it does not exist. You seem to be confusing straight-line motion in an inertial frame with "centrifugal acceleration".

In our ,that is exterior, reference frame...we realize that the
water is forced into movement by the friction between itself and
the bucket.

Sure. That accelerates it both tangentially and radially inward.

Which does not explain in itself whatsoever..why then it is moving from
the central area OUTWARD and UPWARD!

Tom Roberts

Regards, LL

[[Mod. note -- Tom Roberts and others have noted (correctly) that
purely rotational motion involves ONLY a radial acceleration INWARD.
If this were the only motion involved, then the infinitesimal mass
element of water which starts out on the surface at the very center
(rotational axis) of the bucket, wouldn't move.

But the actual water motion during the transient startup phase
(bucket is rotating, but water isn't yet in purely rotational moton)
is much more complicated, involving vortices with mixed tangential
and radial motion.
-- jt]]

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On Wednesday, November 9, 2022 at 4:12:31 PM UTC-5, xray4abc wrote:

On Monday, November 7, 2022 at 1:57:09 PM UTC-5, Tom Roberts wrote:

On 11/3/22 3:39 AM, xray4abc wrote:

On Wednesday, July 13, 2022 at 5:50:42 AM UTC-4, Luigi Fortunati
wrote:

When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal
force.

... only in the rotating-bucket coordinates. In any inertial frame the water does not "accelerate outwards", it merely tries to move in a
straight line -- in the rotating coordinates that is indeed accelerating outward.

But the centrifugal force is ONLY in the rotating reference and
not in the inertial one.

Right. Ditto for any "centrifugal acceleration".

So, how is the centrifugal acceleration of water justified EVEN in
the inertial reference where the centrifugal force is not there?

It isn't justified, because it does not exist. You seem to be confusing straight-line motion in an inertial frame with "centrifugal acceleration".

In our ,that is exterior, reference frame...we realize that the
water is forced into movement by the friction between itself and
the bucket.

Sure. That accelerates it both tangentially and radially inward.

Which does not explain in itself whatsoever..why then it is moving from
the central area OUTWARD and UPWARD!

Tom Roberts

Regards, LL

[[Mod. note -- Tom Roberts and others have noted (correctly) that
purely rotational motion involves ONLY a radial acceleration INWARD.
If this were the only motion involved, then the infinitesimal mass
element of water which starts out on the surface at the very center (rotational axis) of the bucket, wouldn't move.

But the actual water motion during the transient startup phase
(bucket is rotating, but water isn't yet in purely rotational moton)
is much more complicated, involving vortices with mixed tangential
and radial motion.
-- jt]]

I agree, the situation is much more complicated.
But then, this fact has to be stated when an attempt is made toward an explanation! I can see, that even in the classical literature, found in
.. textbooks for an example, oversimplification without honestly
admitting it, is something very common .

Many times..some laws of conservation are invoked.....because the lack
of a thorough understanding of the issues. For an example
.....conservation is invoked when explaining ....the changes in the
rotation of an ice-skater...as if ...the the conservation law itself
could have an active role.

I can explain it without referring DIRECTLY to a conservation law
of a physical quantity. Shortly, it is like this: the rotating body has
its parts (points if you like) moving on circles of a different size
(radius) in the same time intervals. The parts(points) close to the
rotation axis move at lower speed then the ones that are farther, as
they describe smaller circumference circles in the same time than their marginal counterparts. One could say that the rotating body has zones
with low speed close to the axis, and zones of higher speeds going
outwards.

When the skater departs his/her hands......they move from a lower speed
zone into a higher speed zone. (This is .. similar to an inelastic collision....where a redistribution of linear the momentum will take
place.) Then....what the figure-skater does, is.....a redistribution of
his/her body's angular momentum between the different parts of her/his
body ...leading to a reduced speed of the rotation....by changing the
the shape of the body and thus the rotational inertia of it. When they
bring their hands the other way.....the opposite thing happens, that is
...an increase in the rate of spinning.

Best regards, LL

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xray4abc mercoledì 09/11/2022 alle ore 06:12:26 ha scritto:

...
[[Mod. note -- Tom Roberts and others have noted (correctly) that
purely rotational motion involves ONLY a radial acceleration INWARD.
If this were the only motion involved, then the infinitesimal mass
element of water which starts out on the surface at the very center (rotational axis) of the bucket, wouldn't move.

But the actual water motion during the transient startup phase
(bucket is rotating, but water isn't yet in purely rotational moton)
is much more complicated, involving vortices with mixed tangential
and radial motion.
-- jt]]

Okay, in my animation
https://www.geogebra.org/m/qp3aqk5x
I consider a generic water particle at the end of the transient startup
phase, that is, when the water is in purely rotational moton:

The blue centripetal force (on the part of the R particle) and the red centrifugal force (on the part of the S particle) act on the P
particle.

Like the P particle, also all other particles *exert* a centripetal
force on the innermost adjacent particle and (simultaneously) a
centrifugal force on the outermost adjacent particle.

And every single particle *suffers* a centripetal force from the
outermost adjacent particle and (simultaneously) a centrifugal force
from the innermost adjacent particle.

No rotating particle exerts (or suffers) only one of the two forces
and not the other.

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On Thursday, November 10, 2022 at 11:34:06 AM UTC-5, Luigi Fortunati wrote:

xray4abc mercoledÄ=9B 09/11/2022 alle ore 06:12:26 ha scritto:

...
[[Mod. note -- Tom Roberts and others have noted (correctly) that
purely rotational motion involves ONLY a radial acceleration INWARD.
If this were the only motion involved, then the infinitesimal mass
element of water which starts out on the surface at the very center (rotational axis) of the bucket, wouldn't move.

But the actual water motion during the transient startup phase
(bucket is rotating, but water isn't yet in purely rotational moton)
is much more complicated, involving vortices with mixed tangential
and radial motion.
-- jt]]

Okay, in my animation
https://www.geogebra.org/m/qp3aqk5x
I consider a generic water particle at the end of the transient startup phase, that is, when the water is in purely rotational moton:

The blue centripetal force (on the part of the R particle) and the red centrifugal force (on the part of the S particle) act on the P
particle.

Like the P particle, also all other particles *exert* a centripetal
force on the innermost adjacent particle and (simultaneously) a
centrifugal force on the outermost adjacent particle.

And every single particle *suffers* a centripetal force from the
outermost adjacent particle and (simultaneously) a centrifugal force
from the innermost adjacent particle.

No rotating particle exerts (or suffers) only one of the two forces
and not the other.

How about the ones from the extremes, the very end of the radius vector
AND the ones situated one the central symmetry axis? Especially when we
look at.... the spinning of a rigid body!

Regards, LL

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xray4abc venerdì 11/11/2022 alle ore 17:33:24 ha scritto:

How about the ones from the extremes, the very end of the radius vector
AND the ones situated one the central symmetry axis? Especially when we
look at.... the spinning of a rigid body!

Regards, LL

In my new animation
https://www.geogebra.org/m/s9tss84k
there are the particles at the extremes (R and U) and the central
particle (S).

The red forces are centrifugal, the blue forces are centripetal.

Luigi

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On Sunday, November 13, 2022 at 5:10:07 AM UTC-5, Luigi Fortunati wrote:

xray4abc venerd=C4=9B 11/11/2022 alle ore 17:33:24 ha scritto:

How about the ones from the extremes, the very end of the radius vector
AND the ones situated one the central symmetry axis? Especially when we look at.... the spinning of a rigid body!

Regards, LL

In my new animation
https://www.geogebra.org/m/s9tss84k
there are the particles at the extremes (R and U) and the central
particle (S).

The red forces are centrifugal, the blue forces are centripetal.

In most physics textbooks......is considered that ..for a material point to move on a circle

..a centripetal force on it is needed. That particular centripetal force can be exerted from the interior part of that
circle/disc, or of course could be exerted from outside of the circle.
In the majority of practical situations ..the first case scenario applies, because it is the easier one to put in practice. For the liquid in the rotating bucket this centripetal force is due mainly to the bucket itself.
The reaction force to the centripetal force ..would be
the centrifugal force,( in the analyzed case) exerted by the liquid on the bucket.
Let us note that in other cases of rotation, like the rotation of a rigid body-system...the placement of the
forces is exactly the reverse of the situation described above.
For even more clarity, in this last case ..the innermost parts exert the centripetal force (which is the ACTION) and the outermost particles ( where the "every single particle" you mentioned is included as well) exert the centrifugal
force (which is the REACTION).
There are situations of movement on a circle, where is not clear at all, whether the centripetal force is exerted
from inside or from outside of the circle, or how it is exerted at all.
As an example is, the case of the rotation of a charged particle under the effect of the Lorentz force in a uniform
magnetic field, where it is assumed that this particular force is exerted on the entirety of that particle.
The point of all of the above is....a case based analysis is needed for pointing out...who is who..in the world of centrifugal and centripetal forces. One should not just analyze one case and generalize to apply to all other ones,
because it does not work that way.
Now , regarding an earlier posting of mine which was not accepted as one sticking to the subject of this thread, I have to say that , I was disappointed.
Though the subject here seems sort of contained..I hoped that the discussions would eventually lead to
more than just an interesting, yet still very limited, case of rotation.
Best regards, Laszlo Lemhenyi

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