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?
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?
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?
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?
(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
[[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]]
(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
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.
This ratio between the centrifugal and centripetal forces changes when
even the water starts to spin!
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:
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.
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.
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.
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
The difference is: a real force cannot be made to vanish by changing coordinates, while a fictitious "force" will vanish in inertial
coordinates.
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!
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?
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.
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.
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.
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.
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.
...
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 ----
J. J. Lodder alle ore 13:32:02 di mercoledÃ¬ 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?
J. J. Lodder alle ore 13:32:02 di mercoledÃ 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 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).
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.
So in the end, you are stretching the rope.
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.
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
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!
[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 giovedÃƒ 21/07/2022 ha scritto: <snip>It is an error to call that reaction force 'a centrifugal force'.
THERE ARE NO CENTRIFUGAL FORCES.
centrifugal/centripetal [forces] exist in distinct frames of reference,
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.
[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.]
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...You didn't completely describe what you are discussing (your "locally"
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.
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.
IOW: saying "centrifugal forces do not exist" is
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?".
When Newton's bucket starts to rotate, the water slowly starts toCentrifugal forces in rotational reference frames are not
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.
[... repetitions of the above]
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:
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.]
an artifact of the mathematics of using rotating coordinates -- mental constructs of humans are not real.
When Newton's bucket starts to rotate, the water slowly starts toRight!!
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?
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?
In our ,that is exterior, reference frame...we realize that the
water is forced into movement by the friction between itself and
the bucket.
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".
On 11/3/22 3:39 AM, xray4abc wrote:Which does not explain in itself whatsoever..why then it is moving from
On Wednesday, July 13, 2022 at 5:50:42 AM UTC-4, Luigi Fortunati... only in the rotating-bucket coordinates. In any inertial frame the
wrote:
When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal
force.
water does not "accelerate outwards", it merely tries to move in a
straight line -- in the rotating coordinates that is indeed accelerating outward.
Right. Ditto for any "centrifugal acceleration".But the centrifugal force is ONLY in the rotating reference and
not in the inertial one.
It isn't justified, because it does not exist. You seem to be confusing straight-line motion in an inertial frame with "centrifugal acceleration".So, how is the centrifugal acceleration of water justified EVEN in
the inertial reference where the centrifugal force is not there?
In our ,that is exterior, reference frame...we realize that theSure. That accelerates it both tangentially and radially inward.
water is forced into movement by the friction between itself and
the bucket.
Tom RobertsRegards, LL
On Monday, November 7, 2022 at 1:57:09 PM UTC-5, Tom Roberts wrote:
On 11/3/22 3:39 AM, xray4abc wrote:Which does not explain in itself whatsoever..why then it is moving from
On Wednesday, July 13, 2022 at 5:50:42 AM UTC-4, Luigi Fortunati... only in the rotating-bucket coordinates. In any inertial frame the water does not "accelerate outwards", it merely tries to move in a
wrote:
When Newton's bucket starts to rotate, the water slowly starts to
rotate as well and accelerates outwards due to the centrifugal
force.
straight line -- in the rotating coordinates that is indeed accelerating outward.
Right. Ditto for any "centrifugal acceleration".But the centrifugal force is ONLY in the rotating reference and
not in the inertial one.
It isn't justified, because it does not exist. You seem to be confusing straight-line motion in an inertial frame with "centrifugal acceleration".So, how is the centrifugal acceleration of water justified EVEN in
the inertial reference where the centrifugal force is not there?
In our ,that is exterior, reference frame...we realize that theSure. That accelerates it both tangentially and radially inward.
water is forced into movement by the friction between itself and
the bucket.
the central area OUTWARD and UPWARD!
Tom RobertsRegards, 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]]
...
[[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]]
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 phaseOkay, in my animation
(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]]
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
xray4abc venerd=C4=9B 11/11/2022 alle ore 17:33:24 ha scritto:..a centripetal force on it is needed. That particular centripetal force can be exerted from the interior part of that
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, LLIn 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
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