B Rotation is absolute, linear motion is relative?

[A.T.]

You mean like this?
View attachment 320213
If we stop rotate G-room when bucket is at the wall, water in bucket will still spin some time. That is proof that water also rotate about itself during G-room rotation.

Yes if the water is at rest in the rotating frame, it has some angular momentum around the center of the bucket.

Does it mean we must add together effects of water rotation(U shape) plus effects (parabolid shape ) of water circle around Groom pivot point, when G-room is rotate?

You can (but don't have to) decompose the inertial forces like that. But the effect of the circular translation is not a parabolid shape, because the inerial froce field from the centripetal acceleration is uniform. It's a choice of reference frame origin:

A) In the co-rotating frame with origin at the center of the room, you have the following inertial forces:
- Centrifugal force radially away from the room-center (due to rotation of the reference frame axes)

B) In the co-rotating frame with origin at the center of the bucket, you have the following inertial forces:
- Centrifugal force radially away from the bucket-center (due to rotation of the reference frame axes)
- Uniform inertial force parallel to the line connecting the room-center and the bucket-center (due to non-inertial translation of the frame origin)

The sum of the two fields in B must equal the centrifugal force in A. In both frames the water is at rest, so there are no Coriolis forces.

 

[John Mcrain]

No.

in left case bucket is facing allways toward center (roation+circualr motion) and in right case bucket point for example allways to north(only circular motion)
How can then water in bucket behaves the same in this two cases?

 

[John Mcrain]

Yes if the water is at rest in the rotating frame, it has some angular momentum around the center of the bucket.You can (but don't have to) decompose the inertial forces like that. But the effect of the circular translation is not a parabolid shape, because the inerial froce field from the centripetal acceleration is uniform. It's a choice of reference frame origin:

A) In the co-rotating frame with origin at the center of the room, you have the following inertial forces:
- Centrifugal force radially away from the room-center (due to rotation of the reference frame axes)

B) In the co-rotating frame with origin at the center of the bucket, you have the following inertial forces:
- Centrifugal force radially away from the bucket-center (due to rotation of the reference frame axes)
- Uniform inertial force parallel to the line connecting the room-center and the bucket-center (due to non-inertial translation of the frame origin)

The sum of the two fields in B must equal the centrifugal force in A. In both frames the water is at rest, so there are no Coriolis forces.

How can centripetal acceleration be uniform, before you write centrifugal is non-uniform?
Along radius centripetal and centrifugal force must change,so they are non-uniform?

Water in bucket is not point it has lenght, so centrifugal/petal force change along this length?

 

[A.T.]

How can centripetal acceleration be uniform, before you write centrifugal is non-uniform?
Along radius centripetal and centrifugal force must change,so they are non-uniform?

- Inertial centrifugal force due to rotation of the reference frame axes is non-uniform
- Inertial force due to non-inertial translation of the reference frame origin is uniform

 

[John Mcrain]

- Inertial force due to non-inertial translation of the reference frame origin is uniform

But @Ibix write this : Fill the room with water to a depth of a few centimetres and spin it up. The water will settle down into a paraboloid with a minimum at the rotation axis and no bulk motion of the water as seen from the room.

dont understand

 

[John Mcrain]

@A.T.

Outside and inside edge of bucket dont have same velocity and they are not at same place of room radius.
How can that force be uniform?

 

[A.T.]

But @Ibix write this : Fill the room with water to a depth of a few centimetres and spin it up. The water will settle down into a paraboloid with a minimum at the rotation axis and no bulk motion of the water as seen from the room.

dont understand

@A.T.

Outside and inside edge of bucket dont have same velocity and they are not at same place of room radius.
How can that force be uniform?

Read the full post #31 again. In frame B the inertial force has two components, one is non-uniform and one is uniform. The total inertial force in frame B is non-uniform and the same as in frame A.

If you don't get it then stick to frame A. I only mentioned B because you asked if one can decompose the inertial effects like that.

 

[Ibix]

How can then water in bucket behaves the same in this two cases?

So, in one case you've got a bucket on a large turntable and in the other a bucket on a small turntable that is on the large turntable, with spins synchronised so that the bucket maintains its orientation with respect to the lab? I wouldn't expect the behaviour to be the same, except in certain highly idealised cases, due to different frictional forces between the bucket and the water. I wasn't aware you were considering a turntable on a turntable before now.

 

[Devin-M]

You can make a liquid telescope using this principle…

https://en.m.wikipedia.org/wiki/Liquid-mirror_telescope

 

[John Mcrain]

I wasn't aware you were considering a turntable on a turntable before now.

No I didnt consider turntable on turntable in orignal case, I add this example only to point out that rotation of water about itself ( synchronised spin) must have some effect to water shape not just bucket water that is cirlce around pivot point of Groom.

 

[John Mcrain]

Read the full post #31 again. In frame B the inertial force has two components, one is non-uniform and one is uniform. The total inertial force in frame B is non-uniform and the same as in frame A.

If you don't get it then stick to frame A. I only mentioned B because you asked if one can decompose the inertial effects like that.

I still dont understand why both effects are not non-uniform, why in frame of bucket ,cirlce motion around center of Groom is uniform?

 

[Devin-M]

As far as I understand it, if the pilot is holding a bucket while accelerating in a straight line, the surface of the water will be slanted but flat. If he’s holding the bucket somewhere within a centrifuge, it will be slanted and curved. The curvature is the indicator that he’s spinning and not accelerating in a straight line.

 

[A.T.]

I still dont understand why both effects are not non-uniform, why in frame of bucket ,cirlce motion around center of Groom is uniform?

The uniform component is the most basic inertial force due to non-inertial translation of the coordinate system origin: F = -ma where a is the acceleration of the coordinate system origin relative to an inertial frame.

 

[A.T.]

in left case bucket is facing allways toward center (roation+circualr motion) and in right case bucket point for example allways to north(only circular motion)
How can then water in bucket behaves the same in this two cases?

The water surface tends towards an equipotential surface in the rest frame of the water.

Left the equipotential surface in the rotating rest frame of the bucket & water is curved and part of a paraboloid centered on the turn table center.

Right the equipotential surface in the non-rotating but orbiting rest frame of the bucket & water is flat but tilted inwards.

The problem with the right case is that the equipotential surface is not static in the rest frame of the water & bucket, so the water has to flow to follow the equipotential surface. This will lag behind, and create friction with the walls. But ignoring those complications the water surface on the right tends towards a tilted flat plane.

 

[John Mcrain]

The water surface tends towards an equipotential surface in the rest frame of the water.

Left the equipotential surface in the rotating rest frame of the bucket & water is curved and part of a paraboloid centered on the turn table center.

Right the equipotential surface in the non-rotating but orbiting rest frame of the bucket & water is flat but tilted inwards.

The problem with the right case is that the equipotential surface is not static in the rest frame of the water & bucket, so the water has to flow to follow the equipotential surface. This will lag behind, and create friction with the walls. But ignoring those complications the water surface on the right tends towards a tilted flat plane.

So in short,pure orbiting cause tilited flat surface(like in straight line acceleration-dragster) and when we add rotation around itself, then we get tilted curved surface?

 

[A.T.]

So in short,pure orbiting cause tilited flat surface(like in straight line acceleration-dragster) and when we add rotation around itself, then we get tilted curved surface?

Yes, for an idealized fluid that immediately adapts to a changing potential field.

 

[John Mcrain]

Yes, for an idealized fluid that immediately adapts to a changing potential field.

In right case bucket rotate,change orientation in relation to G-room.When G-room stop rotate, water in bucket is calm,not spins.

But for ground frame ,backet is not rotate(change orinetation).

How can different frames get differnet results,isnt rotation absolute?

Or why would rotation be defined to ground frame?

 

[A.T.]

How can different frames get differnet results,isnt rotation absolute?

The two frames are not equivalent precisely because rotation is absolute.

Or why would rotation be defined to ground frame?

It's defined relative to inertial frames.

 

[John Mcrain]

The two frames are not equivalent precisely because rotation is absolute.

It's defined relative to inertial frames.

So I can say moon not change direction in relation to Earth,always same side point toward center of earth?

 

[A.T.]

So I can say moon not change direction in relation to Earth,

That is ambiguous / not clear.

always same side point toward center of earth?

That is correct.

 

[John Mcrain]

That is ambiguous / not clear.

That is correct.

For me moon not rotate because always point toward me, bucket dont rotate in right case from ground frame,bucket dont rotate in left case in relation to G-room frame...etc

everthing is relative, why would one frame be more true then other...From frame that you are looking from,this is correct...

 

[Ibix]

everthing is relative,

Proper acceleration, the kind you can measure with an accelerometer, is not.

why would one frame be more true then other...

Neither frame is "more true". Both will agree on direct observables (e.g. are there forces being applied to the water, or if the bucket rotating with respect to the lab). They may interpret these things differently ("rotating", for example, might mean in the invariant sense where there are detectable forces, or it might mean "rotating relative to me", which might or might not mean in the measurable sense and definitely depends on what frame you are using.).

 

[John Mcrain]

Both will agree on direct observables

For right case ,bucket is rotate in relation to G-room, but not rotate in relation to ground.
Two frames show different results...

 

[A.T.]

why would one frame be more true then other...

Not more true, but simpler with flatter water surface.

 

[jbriggs444]

For right case ,bucket is rotate in relation to G-room, but not rotate in relation to ground.
Two frames show different results...

Any two frames will always agree on all direct observables. Frames of reference are conjured with paper and pencil. They are creations of the mind. They can never have physical effects.

 

[John Mcrain]

Any two frames will always agree on all direct observables. Frames of reference are conjured with paper and pencil. They are creations of the mind. They can never have physical effects.

Is roatation of bucket direct observables?

 

[Ibix]

Is roatation of bucket direct observables?

I would say whether something is rotating or not is determined by whether or not it's feeling a centripetal force. That is a direct observable and something all frames will agree on.

 

[John Mcrain]

I would say whether something is rotating or not is determined by whether or not it's feeling a centripetal force. That is a direct observable and something all frames will agree on.

I only say ,for my right case ,bucket rotate in relation to G-room, but not rotate in relation to ground.
Two frames show different results...
so someone can ask; is water spin in bucket or not...

 

[Ibix]

I only say ,for my right case ,bucket rotate in relation to G-room, but not rotate in relation to ground.

And all frames can agree on those measurements.

Two frames show different results...

No they don't. They differ on whether the buckets ate rotating relative to themselves, but that's because they have different definitions of "themself", not because they have different results.

so someone can ask; is water spin in bucket or not...

They could just look. There can be only one answer. It is well known for a bucket bolted to the floor of the turntable, but harder to calculate for a bucket on a turntable on a turntable, in part because it likely depends on things like the frictional forces between the water and the bucket.

 

[John Mcrain]

but harder to calculate for a bucket on a turntable on a turntable, in part because it likely depends on things like the frictional forces between the water and the bucket.

You mean if friction is zero between water and bucket walls, water will contiue to spin for some time after G room is stoped, for right case?