The Paradox Engine

[Tusk]

Nearly a year with no further comment. Disappointing.

Concept Question 17.2.1 :

http://ocw.mit.edu/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/momentum/systems-center-of-mass-and-conservation-of-momentum/MIT8_01SC_coursenotes17.pdf

There are a few more obstacles to understanding the device but little point covering them in detail before acceptance of this fundamental issue.

I assume that since what was deemed impossible by most is now shown to be possible, the next order of business will be that other impossibility, overunity (strangely, considering the name of this forum).

[broli]

I have not seen this thread before but I commend your experimentation skills. Honestly I have not read the the entire thread but I'm up for discussion.

What you refer as to be the paradox seems to me like it's simple conservation of angular momentum. You accelerate the disk ie increase its angular momentum, since the system is not attached to the earth so to speak, it needs to compensate with an equal change of angular momentum, and thus the whole setup starts to rotate in the other direction. You can get more analytical about it and calculate exactly how much initial linear momentum,angular momentum and kinetic energy you start with and end with. That would show you whether you have a paradox or not.

[telecom]

Since the rotation of the apparatus is caused by the reaction,
it should produce energy equal the input less friction losses, IMHO.

[Tusk]

If the first premise is accepted then there remains only the frame of reference issue. I assume that everyone would be familiar with those roundabouts often seen in the play areas of suburban parks, no doubt most parents have had occasion to spin one around and remember how much force is required. Therefore this is an ideal common point of reference for a hypothetical experiment.

Allow a lightweight wheeled cart on a straight railway track with a roundabout mounted on the cart horizontally (i.e. normal mount) so as to be free to rotate.

Allow that a man is standing next to the roundabout/cart directly to one side so as to be at either the 3 or 9 o'clock position, given that the 6 and 12 o'clock positions coincide with the line of the railway track.

Allow that both the roundabout and the cart are motionless at the start of the experiment.

If the man proceeds to 'spin' the roundabout with a series of applied forces parallel to the railway track we could expect the cart to accelerate along the track as the roundabout accelerates in rotation with each application of force (allowing that the various frictions etc are not sufficient to impede such motion). This outcome can be confirmed by reference to the M.I.T. link in my previous post (prior to this there was only my word on the issue, which understandably left many in doubt).

As the cart accelerates along the track the man must keep pace if he is to continue applying force to the roundabout. Therefore he must not only expend energy on the application of force on the roundabout, he must also expend energy accelerating his own mass in concert with the linear acceleration of the cart; note that the direct reaction to the applied force on the roundabout works against his efforts to accelerate his own mass in concert with the acceleration of the cart. He must not only accelerate his own mass, he must do so against the reaction of any force he applies to the roundabout.

Indeed if the cart had no mass and the entire mass of the roundabout was situated around the outer edge the linear acceleration would match the rotational acceleration (insofar as circular motion may be compared to linear motion). Which would then require as much effort to keep pace with the cart as to spin the roundabout.

Thus far we get nothing for free; no paradox and everything in accordance with the literature. Our man is both pushing and walking/running (against his own 'push') so there are two distinct and separate types of effort on his part, and two distinct motions, linear and rotational, each accumulating energy and storing it as potential energy, less any of the usual losses.

And now we make a small frame of reference adjustment.

Lay the railway track in a circle such that the man stands at the centre, within continuous reach of the nearmost edge of the roundabout as the cart moves around the track. Since he need no longer move other than to rotate on the spot, his efforts will be halved yet the rotational acceleration of the roundabout will actually increase (due to inertial and geometrical factors) while the linear acceleration - converted now to circular motion - remains comparable to the original linear acceleration (insofar as circular motion may be compared to linear motion).

Put simply, the man is now able to achieve a comparable rate of accumulation of potential energy storage in the linear and rotational motions of the roundabout/cart for approximately half the effort (or energy) required in the first instance. So either he was wasting half his energy somehow in the first instance, or he just discovered OU.

And in view of the time of year I will take this opportunity to wish everyone a Merry Christmas and a Happy New Year     



   

 

[broli]

This thread had me thinking again real deeply about angular momentum and all that is attached to it. After also reading your last post a similar "what-if" popped up in my head. I illustrated this.

What you have in the first setup is a big wheel and smaller wheels with motors undernearth attached to it. When the setup is at rest there is no rotation.
However when you start the motors the smaller wheels begin to spin and will have an angular momentum associated to them (green vector). Now because of newton's third law the stator of the motor, which is attached to the big wheel, will experience a counter torque. This counter torque is felt by the big wheel which will start to rotate too. This rotation too will have an angular momentum. It's obvious that this angular momentum is opposite to that of the smaller wheels. Since we're dealing with a closed system the total angular momentum has to remain 0. So nothing unusual here and all makes sense so far.

Now what if we remove the motor from the axles and flip it sideways and let it rotate the wheels by frictional contact. The torque of the axle of the motor will no longer be parallel to the angular momentum vector. We can also forget about the counter torque of the stator as the motor on the other side will spin in opposite direction canceling this torque.
So the only forces we end up with are the frictional contact forces. Unless my reasoning is wrong the only conclusion I end up with is that the bigger wheel will rotate in such a way that its angular momentum will be in the same direction of that of the smaller wheels. That is to say, the angular momentum of the closed system has increased without any outside forces.

Tusk this is basically your electromagnetic experiment however there you tried to get the force dead on the center. And your setup behaved, empirically at least, according to theory. But what happens if you intentionally positioned the motor "in front" or "behind of" the axle. Will the resulting rotation direction of the whole setup always be the same? That I would like to see .

Now I'm eager to hear what high school mistake I made in the previous reasoning .