Seanie

Yes. No explanation here. no explanation here. How is that an explanation for what needs to be explained? How does this even make sense let alone explain the concept? (e.g. momentum in the x-direction is obviously changing because of the constantly varying speed and direction). Yes of course, who wouldn't? You seem to be avoiding the issue. You obviously don't understand the mechanics of the mechanism. That's ok, I have not met anyone yet who does.

Sorry for the confusion. I thought we understood that m1 is a point mass at one end of the rod and m2 at the other end and that they all move as one since they are rigidly connected. This was the model all along so I don't see any inconsistency. So do you know the physics to explain this or what?

Well ok but when I referred to the K.E. of the rod what I meant was the rod including m1 which is part of it.

Otherwise how could anyone be expected to see that the energy is provided by the K.E. of the rod?

I'm referring to the mechanism in its up-to-date form, i.e. with m1 and m2 having mass >0. But isn't it clear that m2 will oscillate? If so then we have not explained where that energy comes from and if it comes from K.E. of m1's rotation we have not shown how that K.E. will be diminished.

This thread has gone very quiet lately. I would like to sum up what I'm aware of thus far re. this mechanism. The unbalanced rotation is made to rotate, this gives rise to the oscillating motion in the x-direction. Newtonian mechanics (NM) does not show any force arising to oppose the rod's rotation. NM provides a straightforward calculation showing that the mechanism produces energy indefinitely. This would be the end of the matter were it not for the belief that conservation of energy must apply somehow. No clear physics has been given here to show how that is. If someone were to propose this mechanism as overunity (I am not doing that, its not allowed here) I cannot show how they would be incorrect. This mechanism needs more investigation to try to solve the apparent mystery. If I am missing something relevant to the main concept kindly share that here but only if you can show clearly and surely the correct physics to explain the mechanism. I hope this little investigation has been helpful and interesting for you, it has been for me. Thank you.

Sorry I don't understand. I don't see how any torque is exerted on either of the masses anyway or how the rod exerts torque. As I see it the rod is freely rotating, so nothing to exert a torque for or against it. Angular momentum is constant, yes I can see how that would be (i.e. since it is not gaining or losing speed). After doing that I see the rod rotating. I may not be getting what you mean. Yes I am aware of that phenomenon but don't see how it applies to the mechanism. The rod does not get shorter (which would be like the ice skater pulling in her limbs).

yes it seems so to me anyway. Ok but how does that happen here? But to my understanding if a rotation (or anything else) changes speed its because some torque (or force) acted against its motion. Otherwise it would seem like a magical happening with no identifiable mechanics to explain it. By all means show me what I'm missing here. If you mean that the rotation may not continue for very long is that because of something about the couple itself? (if so I would love to understand that better), or is it because of friction or what?

If the rod's angular speed changes (i.e. it must slow down) to supply energy to the oscillation then there must be a torque opposing its rotation because from Newton's 1st law it will otherwise continue at the same speed. Or to put it another way, if it slows there must be a force (i.e. torque) or some resistance to its rotation, to slow it. Is that correct? To provide power to the oscillation it seems that m1's rotational energy is the only possible source of that power, yet how does this happen, I mean what are the mechanics of it exactly? Because I don't see a way for there to be such an opposing torque, do you?

Yes, that makes sense too and it is something I had overlooked, thank you. Now I'm wondering what would happen if m2 had a real mass. I suppose m1 would rotate then as well as m2 oscillating. If so then we are back to the old question of where is the torque coming from that would oppose the rod's rotation? If there is none then how to account for the energy to oscillate m2? Yes thanks for the example, I get the idea now. Sorry I thought the answer was contained in what I said here:

Ok, I get what you mean and that makes sense. The only thing is that I don't see how it relates to our mechanism here. To clarify my statement further: so if m1 is the rotating mass, rotating about the point m2 then m2 is the centre of the rotation, that's the "centre being free to move" that I referred to, it is free to move in a straight line in the x-direction. So when m1 is rotating (i.e. an unbalanced rotation) it will tend to pull m2, of course. How is that not the case? With your ball on a string its the same thing, your hand is at the m2 position (centre of rotation) and it will feel a pull towards the ball. Then since m2 if free to move in a straight line it will indeed move, how can it not? If you are saying it will not move that's what I don't understand. Thanks.

I'm not sure what you mean here, it certainly seems a bit derogatory, don't you think? You seem to not like the idea of the rod only being given an initial turning impulse (i.e. without translational force). Why is that? To keep the mechanism as simple as possible so as to focus on explaining what seems to be energy that is unaccounted for (an important matter surely), that's why I specified that the initial impulse only has a rotational effect on the rod about m2. Otherwise we would have to try to calculate the effect of translational force from the initial impulse which would unnecessarily complicate things. I suppose if the initial impulse was a moment that there would also be a translational force and if it were a couple there would not be. Are you clear now about the initial impulse or is there still something other than rotation of the rod that I need to consider (i.e. resulting from the initial impulse)? I'm not sure I get what you mean. We have a rotating mass because it has been given an initial impulse. Then because of its centre being free to move in a straight line the rotating mass will surely pull on its centre, will it not?

because m2 can move even though its KE =0. Also if m2 is moving that means that m1 must have an extra x-direction motion and that requires energy.

We can remove that all we like but we are then stuck with a mechanism that doesn't make sense. I agree. I had been working on similar mechanisms and for some reason had those labels and they just got carried over to this one. Then with all my notes being as they were I didn't want to come up with new names.

That means m2 doesn't have any motion. In that case do you not find it hard to imagine how a rotating eccentric weight would not pull on the centre of its rotation? If it does pull on it and the centre can freely move then why would it not move? I'm hoping that we are at least seeing major problems with our analyses (including mine).

You are correct, the principle here is the same as that of the mechanism in this thread. To make it more fully compatible, make the mass of the cart be zero and the pendulum to swing all the way around and make gravity be zero too. Yes this is also correct but just to be consistent with our mechanism I would have the rod rotating the other way, i.e. rotating clockwise. Also just to clear up any possible doubt about the initial input torque, it is input in a way which doesn't impart any translational force on the rod, it only imparts a turning force.

I was simply telling you what I understand to be true and still hold the same understanding since I haven't reason to change yet. In the case of the torque I said I don't have a particular method in mind, in that case why the need to think I have a bad attitude? And how am I supposed to tell you the method of inputting torque if I don't have a method in mind? I also said it doesn't matter how, because what I meant was that it is not something we should get hung up on given the main thing to be resolved with this mechanism. I think from my post just minutes ago that should be more clear. Then what is wrong with telling you what I said about the scotch yoke? I did give a reason why it is not the same. Do you still not see why they are not the same? Again its the same with the rail, as far as the main focus of explaining the energy source of the oscillation is concerned then it really doesn't matter whether it is above or below. Perhaps your concern for the rail position would be important if we were trying to build a physical model but my understanding of the matter of this thread is that it is about the physics principles involved. I even said it in a nice way. What am I supposed to do? Again my apologies for making you feel dismissed. When our communications are limited to typed text then there's plenty of room for misunderstandings, good if we were discussing this face to face, it should be much better then. If you agree that there will be a motion in the x-direction, i.e. the extra motion as I called it that is the motion of m2, then what force causes that? Do you agree that m2 will oscillate or what do you think will happen? Because whatever that force is will be the same force that causes the reverse. Also that's fine if you don't think it will behave as I suggest but will you kindly explain how it will move then?

I am not being peremptory or dismissive here but I believe I have answered you on this already. Hoping for no bad feelings here so the answer is I don't have a method in mind because I don't see why it is relevant. If you have said something before re. why it is relevant then I'm sure I don't see it, perhaps you can clarify it and/or we can discuss it more if you like. Nevertheless since you are looking for something on this, here is a suggested way: The rod is forcibly rotated anticlockwise against a spring which is not part of the mechanism and released so that the spring accelerates the rod to its initial angular speed. At the same time, to prevent any movement of m2, m2 is held at its starting position until the rod is at its starting angle (theta=0) at which point m2 is automatically released. The spring also does not exert any force on the rod from the moment m2 is released. In that case there should be no force which would cause a translational motion of any part of the rod. Maybe that's why you are asking, to see if the imparted torque imparts any other force. Maybe that's why you asked about the moment and the couple too. Anyway regarding the mechanism the important matter to be dealt with is to explain the still unknown source of energy that powers the anticipated oscillation. If there is a way of inputting the initial torque which could account for the oscillation that still does not solve the apparent mystery of this mechanism, because then I would just change the way the torque is input so it doesn't account for it and we would still be left with an oscillation whose energy source needs to be explained. In this mechanism which is essentially a rotating eccentric weight in which the pivot is free to move in a straight line, then we do have an oscillation caused by that rotation do we not? And so far the explanation of how and where the energy comes from seems amazingly hard to find does it not? Well that's what I am interested in and looking to create awareness of this and to seek the answers. because I believe I specified already that the initial torque is a torque about m2, that would mean there is no force to move the rod bodily as you put it.

I'm not sure how else to show that it will. So if you imagine an unbalanced rotation (i.e. with an eccentric weight rotating) and you constrain the pivot (i.e. centre point of rotation) so it is free to move in a straight line then I suppose you would agree that the pivot will exhibit an oscillating motion on that line, yes? If so then what causes it to oscillate, i.e. to reverse its direction? Where is the force that does that? Well its the same idea with the mechanism I am discussing in this thread. I believe you are mistaken and misjudging me here. I am not aware of a bad attitude with you or them, or of being peremptory. If you give me specific details of your basis for that then that would be fair to me so I can see it for myself it its there and if its not there then I can clarify the misunderstanding for you. Nevertheless I ask your forgiveness if I have offended you. Going forward though I fear that it may easily happen again since I don't know how it happened to begin with, hence my request for you to give details. Thanks in anticipation.

In spite of their fictitious status I find it helpful nevertheless to use the terms centrifugal force and centrifugal acceleration to help understanding of the motion under investigation. Then the centrifugal acceleration of m1 in its "extra" x-direction motion is, understandably, what requires or implies m2's motion. So if m2 is at full speed when theta is pi/2 that's because the centrifugal acceleration is in the same direction that m2 can move when theta is pi/2. All of the centrifugal acceleration is in the positive x-direction at theta = pi/2. Therefore, when you imagine the rotating m1 (or rod) along with m2's freedom of motion in the x-direction you will see that m2 is bound to follow the "extra" x-direction motion of m1 and that since this must be an oscillating motion in the x-direction that means that m2 will have to slow down (theta between pi/2 and pi), stop (theta = pi) and reverse direction (theta >pi), because assuming constant angular speed of m1 for simplicity then theta determines the acceleration for the "extra" motion in the x-direction. Forgive me if I am overstating the explanation but I'm trying to make sure you get it. Another way of saying it is that m1 tends to pull m2 in the x-direction and since m1 is rotating then it constantly changes direction, thus m2 must stop and reverse at certain intervals. To clarify that, I am saying that the initial condition is that the rod is aligned with the positive Y-axis (theta=0). It will not be on top of the Y-axis but parallel to it and will lie along the line x=-r. That is at least if my understanding of m2's x-direction oscillation is correct. From that starting point it possesses its angular speed of w1 (omega 1) and m2 is at the point (-r, 0).

nothing supports it, that's why it is at full speed along the x axis at that point in the rotation.

yes but if one of the two combined motions produces motion in a straight line we may still not see a straight line motion because of the 2nd of the combined motion interfering with the first. For the same reason that tension would be in any rotating rod with a weight on the end. I have described this mechanism and then tried to analyse it to clarify the physics to explain it. I have not succeeded in that and at this stage (long before starting this thread) am stumped by it and really don't know. The explanation seems elusive and beyond me. Finding fault with my analysis is a given. Perhaps you can come up with the correct explanation and be able to show it here. If classical physics is able to explain this then I have still not found anyone (including a number of physics experts) who can. They don't reply to me about it, or they are too busy or don't give it a proper look, or give a partial reply without dealing with the core aspects in need of explanation etc. I have searched exhaustively online for a long time to no avail, likewise in books but nothing. I have been referred to some online resource or book and in the end still find no explanation. Given the relative simplicity of the mechanism, basically just a rotation where the pivot is allowed to move in a line, I find it remarkable that I can not find an explanation. I wonder at what point is it reasonable to decide that classical physics does not have an explanation. If it does not then I'd say that should ring some alarm bells in physics circles. Thanks for bearing with me on this so far anyway and I will continue to try and to live in hope of getting to the bottom of it.

Yes with respect to m2, but it apparently has another motion too which is extra motion in the x-direction, as revealed by the motion of m2 for example. The combination of these two motions produces an ellipse (i.e. m1's locus) and according to my calculations that ellipse is interesting for a few reasons one of which is that it has semi-major and semi-minor axes of phi and 1/phi respectively. Considering there to be two motions of m1 combined, i.e. its rotation about m2 as well as its extra x-direction motion (evidenced by m2's motion) then the "zero net force" you refer to in our case is the zero net centripetal force and indeed the extra x-direction speed is at its maximum when the centripetal force has reached zero, that is equal to m1's tangential velocity in its circular path about m2 and it is when theta = pi/2 radians. Of course the actual (net) motion of m1 is not in a straight line due to the 2nd of the combined motions which it undergoes. I believe what I have said here can be perceived to be true by thinking about it and looking at the diagram. I am now trying to add a better diagram to this post for our convenience, hopefully it is better than the last one I. I still don't see how the circular motion can change its speed as the centripetal force will always act perpendicularly to the rotation. I think swansont made the same point in his recent post. I hope this addresses your points. I'm still having the same problem as before uploading, the word "queued" continues to show all the time and file doesn't seem to upload. I will try putting the file where I put the last one and maybe someone here can add it here like before. Diagram is at https://ibb.co/NjTmVb1

I may not be able to prove that it moves exactly the way described. So let's see what aspects of its motion could reasonably be doubted. With a given rotation of the rod m2 will surely oscillate about the origin, that seems self-evident, is it not? Then consider two cases: 1. If w1 remains constant: Then m2's oscillation will surely be simple harmonic about the origin, will it not? If so then it moves as described. If not then how does m2 move? Also, regardless of whether the oscillation is simple harmonic there will surely be an oscillation which at least approximates simple harmonic will there not? Then even with any acceleration of m2 there must be energy to make that happen and apparently the only place that energy can come from is from the rotational kinetic energy of m1 which means w1 must be reduced but that is not an option here because in this paragraph it is assumed that w1 is constant. Therefore, logically, m2 cannot move at all and it seems self-evident that this cannot be the case. So then if m2 moves and the rod has a constant w1, where is the energy coming from? 2. If w1 changes: If m2 were fixed at the origin then clearly by Newton's first law w1 will remain constant. Therefore with m2 moving and since w1 changes (assumed in this paragraph) and such change must be a reduction, that means the motion of m2 must somehow be able to effect this change in w1. In this case the motion will differ from what I assumed it to be only in the reduction of w1 until the rod stops rotating. In that case also it must be that the energy for m2's motion comes from the rotational kinetic energy of m1, and with a diminishing w1 that seems plausible. Still the physics of how that happens needs to be worked out. It seems to me that the rod will experience a tension which varies from zero to a maximum according to theta. So when theta = 0 (i.e. rod extending from the origin along the positive y-axis) the rod will momentarily be rotating about what is essentially a fixed point (m2 at the origin), therefore the standard formula for centripetal force applies. As the rod rotates past this point (i.e. theta > 0) m2 will begin to move in the positive x-direction and thereby increasingly reduce the tension in the rod. By the time theta reaches pi/2 radians the rod will not offer any resistance to m1's (or m2's) motion in the positive x-direction and so the tension will be zero. For theta > pi/2 the tension will rise again until it reaches a maximum at theta = pi radians, and so on. I don't see how there will be any compressive force on the rod. What do you think?

I am grateful for your efforts to explain the mechanism under discussion. However I would like to point out a couple of things: 1. All of that about the position of the rail under or over the rod is irrelevant to the principle involved here. That's because as long as the rod moves as I described then there is the need to explain the apparent power in m2's motion in spite of an absence of power being input to the rod's rotation. That is the issue. 2. The mechanism under discussion here is fundamentally different from a scotch yoke. In the mechanism here the power in m2's motion is not being taken from the rotational kinetic energy of the rod, at least not that has been shown yet. In the scotch yoke the yoke's motion is clearly being powered by the rotational kinetic energy of the rod or crank. The crux of the matter here is to explain where the power comes from which causes m1 to have a constantly changing acceleration in the x direction.