studiot

You have missed out some parts of the system in your analysis. ie you have omitted some of the forces acting. 1) You say the magnets 1, and 3 are rigidly fixed on the bar, whilst the bar slides through magnet2 without friction. OK but unless you apply a restraining force the bar will slide so that it is centralised in M2 positioning M1 and M3 equidistant from M2. If this restraining force is provided by M4 then a new equilibrium will be established somewhat as you have drawn it. 2) If you apply a force displacing the system from this equilibrium position (and you will have to) your force will do work against the opposing magnetic forces. 3) I was recently at the Science Centre exhibition in Dundee where they have several magnetic displays set up. One had two bar magnets like yours mounted on pegs near each other so they could spin freely. Aligning them as M1 and M2 causes one to spin rapidly, the spin being transfered back and fore between the two magnets until they lock in equilibrium with opposing faces in opposition. The point of this was to note that each magnet will be subject to moments on its mounting, which you also have not accounted for in your list of forces acting.

Thnak you for your response, tar. The introduction of a fictitious centrifugal force is a valid (though currently frowned upon) method of solving certain problems in physics / engineering. For instance it will enable you to calculate the tension in a string whirling with a weight on the end. This is so because it reduces a dynamic problem of a system that is not in equilibrium to a static one where the system is in equilibrium. However the string and weight is a particularly simple system with very few forces acting. Rotodynamic machines (pumps and turbines) are much more complicated systems where the addition of a fictitious centrifugal force does not put the system into equilibrium. In such cases D'Alembert's method is inappropriate and cannot be used to explain the workings of such machinery. Additional forces act between the casings, the fluid and the impellors.

Mike may have been a victim of the engineering education system 30 to 50 years ago when they were teaching this stuff. But no one has commented on my post#329 where they are still teaching it today.

In another thread you argue against monculture. Sustainability and ecology are also susceptible to this argument against single ideas/panaceas. Decentralisation is also largely responsible for the huge increase in vehicle journeys undertaken by modern citizens, going to school, work, play and other activities. But then there is there is the 'Transition Town ' movement. One of its founders Totnes in Devon went so far as to have its own currency. I recently attended a fascinating lecture by Professor Ioan Fazey of Dundee University Institute about sustainability in the Solomon Islands. The study showed some suprising effects.

I would have said you are into modular arithmetic and that A can acquire T, what ever the angular speeds, by this method. If this is so then there is no safe speed for T.

There are alternative (and IMHO more sensible) views on current policies on many waste products, not just sanitation waste

A stopped clock is exactly correct twice a day. It takes one circuit by A for T to aquire A's angular velocity or cycle time. T can then fire at the appropriate point of A's second circuit to score a hit, whatever the angular velocity of A.

What do you mean by track, if T1 is fixed?

The interesting thing about imatfaal's video is the question How does the cup of tea get past the cycle forkhead?

It is interesting to note that at least one respected technical university is still teaching centrifugal force as a real force, to engineers. See here from the University of Newcastle Department of Chemical Engineering. 2.1.1, line 1) http://lorien.ncl.ac.uk/ming/particle/cpe124p2.html

Here is an interesting sequel to imatfaal's experiment, courtesy the University of Illinois. https://van.physics.illinois.edu/qa/listing.php?id=14308

I don't see how any of the suggestions would help with my hardness example. The OP was careful to specify that

It is difficult enough to follow these posts without using acronyms or other abbreviations so please write out your posts in full. It is still not clear what you mean by DES. Bignose did not hazard a guess at Differential Equation Systems, (Read his post again). There is a big difference between what I understand by "Systems of Differential Equations" and A system that can be represented by one or more differential equations. Much development and use is made in modern applied maths of the fact that any differential equation can also be written as an integral equation, So yes there are alternatives. Look up the Operational Calculus, Functional analysis and more. Perhaps now would be a good time to include in your next response a definite example of what you are trying to solve.

Please explain your aim in more detail. You have said that the results are two different methods of measuring some property and that they cannot be interconverted. Since they cannot be interconverted what do you want us to do? I can think of a situation like this with hardness measurements where there is no direct correlation between the Mohs, Vickers and Brinell scales and the units have differenct physical dimensions. Is your situation like this?

If this were a science story then would we not approach it more rigourously? 1) Theoretical perpetual motion is required, not forbidden by the laws of mechanics. 2) The laws of Thermodynamics proscibe two types of perpetual motion machines or processes. The first proscription concerns the first law and I would hazard a guess that the problem here is the age old error of improperly defining the system boundary, leading to inappropriate conclusions. The second proscription concerns only cyclic processes or machines. This proscription does not apply to parts of a cycle. If I could obtain a proper description of what the OP is proposing I could comment further but I fail to see either a definite system boundary or a cyclic machine or process described in the material presented.

Here is an a video of a glass of liquid during an airplane roll. https://www.youtube.com/watch?feature=player_detailpage&v=uw2qPLEgKdQ#t=3

I wondered about that, I didn't think of a bicycle, though I've just pumped up a tyre this afternnoon. +1 I haven't the resources to do any graphics until June. BTW I also never knew St James berries were red

Thanks for the video, Google didn't find it for me.

We have had umpteen threads about forces and accelerations on rotating bodies, without result, so here is a question for those who think they know. Put a cup, half full of tea, on the outer edge of a motorised lazy susan and spin. What will happen to the surface of the tea in the cup. Will it rise up one side, if so up the inner (close to the centre) or the outer? What does this mean for the centrifugal v centripetal argument? I have tried to find a video of this experiment without success. I can only find videos showing the vortex created by spinning the cup about its own axis. So I woudl be grateful if anyone can offer one.

In fairness to overtone, I have observed the application of the 'rules of the scientific method' to be subjectively applied generally (including on this forum) in support of a particular person's view. That is, unfortunately human nature. It is really difficult to be truly objective. Here is a good summary discussion of the scientific method, including the difference between deductive and inductive routes. There are also good sections on the limitations of the method, types of evidence and fallacies. http://www.scientificpsychic.com/workbook/scientific-method.htm

The 2012 James Mackenzie lecture at the Royal College of General Practitioners by the late Professor Helen Lester has much of worth to add to the OP story. Actual facts, figures and most of all, compassion. The first few minutes of the lecture https://www.youtube.com/watch?v=tqyACm5OQOM

I have ignored other minor errors as typos anyone could make, and I make all too often. However for someone to preach to me about the English language and any connection it might have to Mathematics should start by getting his facts right, not wrong and then repeating that error. What is an explanation mark? The problem about discussing or not discussing your ideas as I see it is that, whilst on the one hand you are inviting comment, on the other you are making contradictory statements about any comment and being quite rude about it. ajb, in particular, has offered you some mathematical insight taking mathematics beyond the simple definitions that could be entirely applicable if your ideas were serious. That you reject them out of hand suggests to me you are not, but simply trolling.

'Straight' is a modern translation of what Newton actually said "In its right line" Which will actually satisfy the requirements of geodesics on in a manifold, which simple 'straight' would not. A straight line in 3D is described by the intesection of two planes and therefore satisfies the equations of both of them simultaneously. There is not one single equation to describe a straight line in 3D (euclidian space), but a pair of simultaneous equations.

And what does truly straight mean?

Immediately behind the gun of course, since it is well known that immediately in front of the gun is the safest place on the firing range.