12 times more output than input, dual mechanical oscillation system !

[Bubba1]

Problem is, starting from the same level, both cases will finally oscillate. The lever case, however, will make two additional full turns which the wheel with weight attached to rim won't. Focus on this effect. That's the important observation in this case.

In the case of the lever, in going around a full turn, the weight WILL NOT GET BACK UP TO ITS ORIGINAL HEIGHT, so naturally it has some extra kinetic energy.  Focus on that.

[Omnibus]

In the case of the lever, in going around a full turn, the weight WILL NOT GET BACK UP TO ITS ORIGINAL HEIGHT, so naturally it has some extra kinetic energy.  Focus on that.

The focus here should be the fact that in one case the disc cannot make even one full turn while in the other case the disc makes two full turns and much more. To convince yourself that that's the case adjust the initial height and the final height in the two cases exactly the same. By the very nature of the devices it will turn out that the same potential energy in on case cannot even finish a turn while in the other causes almost three turns. So, yes, the potential energies in the two cases which are the subject of comparison are exactly the same. The kinetic energies derived from these equal potential energies, however, differ substantially. That's the issue, nothing else.

[fletcher]

The focus here should be the fact that in one case the disc cannot make even one full turn while in the other case the disc makes two full turns and much more. To convince yourself that that's the case adjust the initial height and the final height in the two cases exactly the same. By the very nature of the devices it will turn out that the same potential energy in on case cannot even finish a turn while in the other causes almost three turns.

So, yes, the potential energies in the two cases which are the subject of comparison are exactly the same.

The kinetic energies derived from these equal potential energies, however, differ substantially.

That's the issue, nothing else.

Your statement about Pe's be exactly the SAME is blatantly incorrect !

Assuming both start at the same height then their Pe [mgh] is calculated on displacement from a datum.

In the case of the mass attached to a rim & released that bottom datum is the axle [Center of Rotation] because the CoM orbits around this point at constant radius - thus height is h1.

In the case of the hanging pendulum wheels the datum moves to below the axle i.e. h is greater - the CoM doesn't orbit at a constant radius about the CoR but an elliptical path, so height = h1 + h2, giving greater Pe [mgh].

[Omnibus]

I said, you will adjust the heights to be the same in both cases. Otherwise you can't compare them. The point is that with a weight attached to the rim, no matter what you do and what height you choose you won't be able to achieve almost threefull rotation starting from rest. With a lever construction you can for almost any height you choose.

This is a difference in behavior which is obvious even qualitatively and that's one of the direct demonstrations of CoE violation.

[fletcher]

I said, you will adjust the heights to be the same in both cases. Otherwise you can't compare them. The point is that with a weight attached to the rim, no matter what you do and what height you choose you won't be able to achieve almost threefull rotation starting from rest. With a lever construction you can for almost any height you choose.

This is a difference in behavior which is obvious even qualitatively and that's one of the direct demonstrations of CoE violation.

The focus here should be the fact that in one case the disc cannot make even one full turn while in the other case the disc makes two full turns and much more.

To convince yourself that that's the case adjust the initial height and the final height in the two cases exactly the same. By the very nature of the devices it will turn out that the same potential energy in on case cannot even finish a turn while in the other causes almost three turns.

So, yes, the potential energies in the two cases which are the subject of comparison are exactly the same.

My misunderstanding of what you wrote then about initial & final heights.

However you continue to conveniently forget that you had to raise the pendulum to create the torque & that took Input Energy - the wheel may achieve a few rotations but it does not restore Pe to starting conditions or self sustain itself.

Since you Inputted Energy to give it Pe max, but it did not achieve restoration of Pe, but did have residual Ke & lower Pe, then I would hardly call that "one of the direct demonstrations of violation of CoE".

The Pe shortfall equals the residual Ke of the wheel allowing a few turns before frictions cause it to keel. - Nothing at all special there !


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If there were a violation of CoE then there should be surplus Energy available to do Work !

Where is it & make the wheel do continuous work whilst sustaining itself ? - otherwise it's a weighted chain pendulum clock analogue ?