Centrifugal forces + pressure and CG
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Take half torus with solid part of density 1, other half torus with liquid of density 1. The torus turn at W rd/s enough for maintain liquid at external circle. Now, for 0 to 180° we accelerate torus, this increase forces (blue in drawing) from pressure of water and from 180° to 360° we deccelerate torus. Rotationnal speed change from W to W+w to W. It's like torus change the CG without external forces. I thought solid give pressure too but I can imagine 2 liquids with different density, it's the same. I have some questions:
1/ water don't give pressure so no force exist ? 2/ solid give same pressure ? 3/ when we rotate the forces from rotation, this cancel pressure forces ? Edit: I add another drawing for show different positions 
Re: Centrifugal forces + pressure and CG
Maybe my questions are not precise enough ?
When I drawn solid in black, it's possible to imagine it maintain from center of circle with solid like this no pressure can appear from solid (imagine a lot of smal ropes for maintain all part of solid). So if solid don't give pressure, it is liquid that don't give pressure ? 
Re: Centrifugal forces + pressure and CG
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Does this attachment help?
There is certainly a tangential ring pressure developed in a rotating ring. In a solid it is a stress and in a liquid it is pressure. Of course these are equal in your ring because the densities are equal. For unequal densities you would have to relocate the centre of mass. 
Re: Centrifugal forces + pressure and CG
I don't understand exactly what you are doing here, but one difference between the solid and liquid parts is that there must be a container that holds the liquid, and the container will apply a force to the liquid. If you ignore that fact, you will get the wrong forces and stresses.

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Re: Centrifugal forces + pressure and CG
This is actually a very complicated problem. Based on lots of experience in fluid and solid mechanics modelling, I can tell you that the best way to approach a problem like this is to start with some much simpler versions of the problem, and solve them first, and gradually add complexity until you get to the actual problem you are trying to solve. Why? First of all, if you can't solve the simpler versions of the problem, you certainly won't be able to solve the more complex problem. Secondly, you will gain understanding along the way from the solutions to the simpler problems.
In the system you describe, neither the solid nor the liquid will behave as a rigid body. Both will experience transient nonhomogeneous deformations. The liquid will exhibit viscous flow that has to be accounted for, and the solid will exhibit elastic deformation that has to be accounted for. I suggest starting out with the following very simple problem: Consider an infinitely long straight pipe containing a viscous fluid. Initially the pipe and the fluid are at rest. At time zero, the pipe is set in motion with a steady velocity V along its axis. What is the velocity and pressure distribution within the fluid as a function of time and radial position? If you can't solve this problem, you will never be able to do the torus problem. As a second version of the problem, consider the same pipe and fluid, but this time make the imposed pipe velocity a function of time. As a third problem, consider the case where there are rigid plugs within the pipe, and a finite length of fluid between the plugs. The plugs move with the pipe velocity. 
Re: Centrifugal forces + pressure and CG
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With W=constant, are there forces from liquid ? I think forces from solid can't be near 0 if there is a lot of parts (imagine infinite number of parts and ropes). Even if there are forces from liquid is strange because even on a round forces cancel themselves if we place this system on another object in a part of time (60° for example), this change the CG of object I think. For change velocity, we can change the rotation of the system or place a lot of stems for help solid and liquid to gain velocity very quickly. In theory, if velocity is apply on each atom of liquid and solid, forces are centripetal forces only. 
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The boundary conditions are the key to the actual stress distrubition. For a rotating solid thin ring or cylinder with no radial constraints imposed, the main stress compoent is tension around the circumference of the ring. But a fluid can't sustain any significant tensile stress (or negative hydrostatic pressure if you prefer to call it that), so there must be some radial constraint forces (for example the fluid pressure on the solid structure that is containing it) to make the situation physically realistic. 
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Re: Centrifugal forces + pressure and CG
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Could any of these forces apply to the earths core?

Re: Centrifugal forces + pressure and CG
1/ I would like to know if there are forces from pressure of liquid when W = constant ? AlephZero said that container would give the same force but that force come from the support of the system, right ? So the system oscillate around a point, the CG move ?
2/ If W varies with time, it's easy to change the system for accelerate/deccelerate not the support of the system but a lot of parts of solid and liquid for reduce problem from deformation I think. @Studiot: Quote:
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AZ did say Quote:
So let us take things one step at a time. Do you understand the idea that any rotating object will be subject to internal forces that can be resolved in two directions at right angles  radially and tangentially? 
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Re: Centrifugal forces + pressure and CG
Which direction do you think angular momentum acts?

Re: Centrifugal forces + pressure and CG
(I want to understand first when W = constant) it's tangential but I don't see how forces come from on your drawing at message #3

Re: Centrifugal forces + pressure and CG
We were discussing circumferential (tangential) stresses in rotating discs recently here.
http://www.physicsforums.com/showthr...light=rotation 
Re: Centrifugal forces + pressure and CG
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Maybe for me it's easier to understand with small solid deformable material. I imagine a part of sector like drawing show. The material is solid but deformable. The deformation put pressure at right and at left, where is the C force in your message #3 ? The deformation is more and more high at external circle.

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