- #1
Q-reeus
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A while back I piggy-backed onto another thread (and then withdrew it as being out of place) an example of a system possibly violating the conservation of energy and momentum (angular momentum directly) - a spinning hollow right circular cylinder placed under frictionless axial compression. Many of you will remember it, but only one attempt at a detailed response was offered, and no firm conclusion. Anyway, by means of a cyclical process exploiting the path-dependent system properties, it was argued angular momentum and kinetic energy could be built up indefinitely - all by exploiting the Relativistic properties of pressure applied to a solid transverse to the direction of motion. A simplifying assumption was notional 'incompressibility' of the cylinder, which although used in many such gedanken experiments without any fuss, might owing to the 'controversial' conclusions, be somehow considered suspect here (and indeed finite compressibility does admit to a counteracting effect, but not one that 'balances the books'). So now for mark II - finite compressibility allowed, and where now both continuous and cyclical 'violation of fundamental physics' seem possible:
Consider then a typical disc 'brake' setup, modified in that the pair of 'brake' pads that clamp with equal and opposite force to the flat surfaces of the disk, are notionally frictionless; functioning to apply transverse pressure to the disk area under the pads but inducing no appreciable braking torque. Take the disk rotation axis as horizontal, and the pads placed such that a line drawn between their center of pressure and the disk spin axis connects horizontally also. Initially suppose the disk is unclamped and spun up to some constant rotational speed. Earth's gravity acts on the disk but by symmetry there is no resultant torque about the spin axis. Now apply transverse pressure via the pair of pads. Compressive stress and strain acts on the patch of disk under the pads, so therefore an appreciable elastic energy density over some volume, hence an increased mass, proportionally essentially to the square of the applied pressure. Additionally, there is formally at least an additional contribution from the first power of the transverse pressure alone, independent of any elastic deformation. So we have in effect an 'overbalancing wheel' - via transverse pressure there is induced more mass on one side of the disc than the other. Coupled to Earth's gravity this gives rise to a steady torque about the spin axis and thus rotational free
energy' - depending of course on the rotational sense. That's the steady part.
As for the rotating cylinder first mentioned, we could also arrange a cyclical process in which the disk is spun up unstressed and then spun down stressed. Taking advantage now of the increased inertial mass when stressed there is a net gain in both angular momentum and rotational KE per cycle. And given that the system as a whole is gaining mass/energy, clearly in any other inertial frame conservation of linear momentum fails, and angular momentum becomes completely arbitrary.
One might initially entertain one further 'violation' - in the steady rotation regime the patch of increased mass is subject to continual centripetal acceleration and centrifugal force, suggesting the system will move off in direct violation of conservation of linear momentum in that frame. However we note that there will be 'fringing' at the leading and trailing parts of the transverse stress field induced in the disk - hence symmetrically disposed longitudinal components of stress exist. Formally then we suppose these longitudinal components allow 'back reaction' forces at the entry and exit regions according to Fbr = -dp/dt = -v*dm/dt (m being that from integrating over the non-uniformly stressed regions), which although equal in magnitude by symmetry, are not exactly collinear, and so a net resultant opposes the centrifugal part. An exact analysis would not be easy, and full cancellation is only a hypothesis here. Given what else here does not seem to hold 'as expected', there may be room for some doubt!
Wow, so is there some obvious flaw to all this? Constructive feedback welcome but please, avoid using high-end maths theorems unless they are applied to the specifics of the scenarios given above. :zzz:
Consider then a typical disc 'brake' setup, modified in that the pair of 'brake' pads that clamp with equal and opposite force to the flat surfaces of the disk, are notionally frictionless; functioning to apply transverse pressure to the disk area under the pads but inducing no appreciable braking torque. Take the disk rotation axis as horizontal, and the pads placed such that a line drawn between their center of pressure and the disk spin axis connects horizontally also. Initially suppose the disk is unclamped and spun up to some constant rotational speed. Earth's gravity acts on the disk but by symmetry there is no resultant torque about the spin axis. Now apply transverse pressure via the pair of pads. Compressive stress and strain acts on the patch of disk under the pads, so therefore an appreciable elastic energy density over some volume, hence an increased mass, proportionally essentially to the square of the applied pressure. Additionally, there is formally at least an additional contribution from the first power of the transverse pressure alone, independent of any elastic deformation. So we have in effect an 'overbalancing wheel' - via transverse pressure there is induced more mass on one side of the disc than the other. Coupled to Earth's gravity this gives rise to a steady torque about the spin axis and thus rotational free
energy' - depending of course on the rotational sense. That's the steady part.
As for the rotating cylinder first mentioned, we could also arrange a cyclical process in which the disk is spun up unstressed and then spun down stressed. Taking advantage now of the increased inertial mass when stressed there is a net gain in both angular momentum and rotational KE per cycle. And given that the system as a whole is gaining mass/energy, clearly in any other inertial frame conservation of linear momentum fails, and angular momentum becomes completely arbitrary.
One might initially entertain one further 'violation' - in the steady rotation regime the patch of increased mass is subject to continual centripetal acceleration and centrifugal force, suggesting the system will move off in direct violation of conservation of linear momentum in that frame. However we note that there will be 'fringing' at the leading and trailing parts of the transverse stress field induced in the disk - hence symmetrically disposed longitudinal components of stress exist. Formally then we suppose these longitudinal components allow 'back reaction' forces at the entry and exit regions according to Fbr = -dp/dt = -v*dm/dt (m being that from integrating over the non-uniformly stressed regions), which although equal in magnitude by symmetry, are not exactly collinear, and so a net resultant opposes the centrifugal part. An exact analysis would not be easy, and full cancellation is only a hypothesis here. Given what else here does not seem to hold 'as expected', there may be room for some doubt!
Wow, so is there some obvious flaw to all this? Constructive feedback welcome but please, avoid using high-end maths theorems unless they are applied to the specifics of the scenarios given above. :zzz:
