# Newton's bucket

225 views

### Luigi Fortunati

Jul 13, 2022, 5:50:42 AM7/13/22
to
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?

### Richard Livingston

Jul 13, 2022, 3:13:27 PM7/13/22
to
"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.

### Julio Di Egidio

Jul 14, 2022, 1:29:46 AM7/14/22
to
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

### J. J. Lodder

Jul 14, 2022, 9:58:45 AM7/14/22
to
This is either completely trivial,
or one of the great mysteries of physics,

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.

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.

### Luigi Fortunati

Jul 14, 2022, 7:57:10 PM7/14/22
to
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]]

### Phillip Helbig

Jul 15, 2022, 10:37:46 AM7/15/22
to
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.th...@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

### Luigi Fortunati

Jul 15, 2022, 10:44:55 AM7/15/22
to
Luigi Fortunati alle ore 11:57:05 di giovedě 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!

### Jonathan Thornburg [remove -color to reply]

Jul 15, 2022, 10:45:58 AM7/15/22
to
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

### Julio Di Egidio

Jul 15, 2022, 7:11:23 PM7/15/22
to
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

### Tom Roberts

Jul 15, 2022, 7:11:33 PM7/15/22
to
(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

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).
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

> 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

### Luigi Fortunati

Jul 17, 2022, 4:04:06 PM7/17/22
to
Tom Roberts alle ore 11:11:21 di venerdě 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.

### Tom Roberts

Jul 17, 2022, 4:04:06 PM7/17/22
to
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

### Julio Di Egidio

Jul 18, 2022, 2:39:00 AM7/18/22
to
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

### Luigi Fortunati

Jul 18, 2022, 5:50:31 AM7/18/22
to
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?

### Tom Roberts

Jul 18, 2022, 3:14:25 PM7/18/22
to
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

### Tom Roberts

Jul 18, 2022, 3:14:37 PM7/18/22
to
On 7/17/22 12:54 AM, Luigi Fortunati wrote:
> Tom Roberts alle ore 11:11:21 di venerdė 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.

Physical phenomena are necessarily independent of coordinates. But the
description/explanation will often depend on coordinates, and in this

Tom Roberts

### J. J. Lodder

Jul 19, 2022, 4:18:44 AM7/19/22
to
Jonathan Thornburg [remove -color to reply] <dr.j.th...@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)

### J. J. Lodder

Jul 19, 2022, 6:28:21 AM7/19/22
to
Phillip Helbig <hel...@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

### Luigi Fortunati

Jul 20, 2022, 2:39:29 AM7/20/22
to
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

### J. J. Lodder

Jul 20, 2022, 7:32:05 AM7/20/22
to
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,
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

### Luigi Fortunati

Jul 21, 2022, 7:17:26 AM7/21/22
to
J. J. Lodder alle ore 13:32:02 di mercoledì 20/07/2022 ha scritto:
> ...
> Perhaps the method employed by my high school teacher,
> 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?

### Torn Rumero DeBrak

Jul 21, 2022, 9:59:07 AM7/21/22
to
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.

### J. J. Lodder

Jul 21, 2022, 9:59:37 AM7/21/22
to
Luigi Fortunati <fortuna...@gmail.com> wrote:
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)

### Tom Roberts

Jul 22, 2022, 3:06:17 AM7/22/22
to
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

### Luigi Fortunati

Jul 22, 2022, 3:06:17 AM7/22/22
to
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?
>
> 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!

### J. J. Lodder

Jul 22, 2022, 7:04:58 AM7/22/22
to
[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 <fortuna...@gmail.com> wrote:

> Torn Rumero DeBrak alle ore 15:59:04 di giovedÃ 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

### Julio Di Egidio

Jul 22, 2022, 1:39:58 PM7/22/22
to
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 giovedÃ 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

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

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

### Thomas Koenig

Jul 23, 2022, 5:49:19 AM7/23/22
to
> [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.

### Tom Roberts

Jul 23, 2022, 5:49:19 AM7/23/22
to
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

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

Tom Roberts

### Julio Di Egidio

Jul 25, 2022, 1:44:54 AM7/25/22
to
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
> 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

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.]

### Luigi Fortunati

Jul 25, 2022, 3:01:22 AM7/25/22
to
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?".

### J. J. Lodder

Jul 25, 2022, 5:06:55 AM7/25/22
to
Luigi Fortunati <fortuna...@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

### mano4848

Sep 22, 2022, 4:18:21 AM9/22/22
to
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)

### xray4abc

Nov 1, 2022, 3:44:18 AM11/1/22
to
[[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