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Another interesting point is a symmetrical angular momentum. During repulsing action just one object has an angular momentum. Base on law of momentum conservation the isolated system should have the symmetrical angular momentum. However no any other physical objects have it. Base on modern classical mechanic, this symmetrical angular momentum is exist potentially if calculated distance between center mass of isolated system and center of mass of objects. But here both objects induce together this symmetrical angular momentum from theirs translational momentums cancel and their linear kinetic energies conversion to rotational kinetic energy. But where is another energy which came form symmetrical repulsing action for angular momentums when symmetrical forces repulse objects?

Or, if repulse two objects symmetrically away from theirs center of mass then both objects will have same linear momentums and same angular momentums.
However, another unpaired potential asymmetrical angular momentum is exist between center of mass of isolated system and objects center of mass during their linear momentum cancel. This could be explained by same sentence. The consequence law of momentum conservation where objects have symmetrical behavior should not be used for this objects repulsing case.

The previous post is not correct.
If objects have symmetrical actions then the consequence from third Newton's law works always. However, the consequence form third Newton's law where objects have asymmetrical behavior must be confirmed by experiment.

http://knol.google.com/k/paradox-of-classical-mechanics-2#
For example, the rotated object gets more kinetic energy on experiment 2 rather than this non rotated object on experiment 1. It means, for this rotated object, like on experiment 1 one force is conducting work for translational motion only and another force(torque) is conducting work for rotational motion only. Base on third Newton’s law, these forces must have symmetrical reaction forces. These symmetrical reaction forces are applying to other non rotated object which conducts translational motion only. Unfortunately, the modern classical mechanics use trivial consequence from third Newton’s law where objects have symmetrical behavior. Base on this model, look through center of mass of isolated system these two objects are getting symmetrical linear and angular momentums with symmetrical behavior on repulsing action. However, different objects alignment brings asymmetrical behavior of these objects. The non rotated object does not conduct rotational motion around center of mass of isolated system. Therefore, these objects asymmetrical behavior cannot be described by trivial consequence of third Newton’s law.

Return back to Wheels problem
http://knol.google.com/k/alex-belov/the-wheels/1xmqm1l0s4ys/18#

This figure shows more realistic model where rolling objects with same mass have different velocities after repulsing action.

Do they really? The wheels on the left receive more energy because the spring applies the same force for the same time, but moves through a greater distance. That extra energy can just go into spinning them faster than the wheels on the right.

Ok.
http://knol.google.com/k/alex-belov/the-wheels/1xmqm1l0s4ys/18#
This problem description use weightless spring and platforms.
You can't count problem backwards from consequence. It must counted directly from third newton's law. Base on this law the net forces of both sides must be identical. The more realistic digram doesn't let platforms conduct rotational and translational motion. Just translational motion only. Base on kinematic equations for rolling bodies on surface, the net force of each side will be the sum of force which applied for translational motion of rolling objects plus torque which apllied for rotation motion divided by radius of rolling bodies. It shows on my solution. Base on this equation the rolling bodies with different moment of inertia have a different translational and rotational accelerations.
For instance, classic problem for rolling bodies on incline shows, the rolling bodies with same mass and different moment of inertia have a different translational acceleration on the end of incline.
Here's same situation. The rolling bodies with same mass and different moment of inertia have different translational acceleration during repulsing action.
This problem shows paradox of classical mechanics where third newton's law of symmetry of interactions does not follow into consequence of simple law of momentum conservation. The modern law of momentum conservation in simple form works just for trivial cases where objects have symmetrical motion behavior. On other objects asymmetrical behavior during interaction, the law of momentum conservation has a complex form.
http://knol.google.com/k/paradox-of-classical-mechanics-2#
This is not unique mistake on physic. Similar mistake into quantum mechanics, where trivial consequence of supersymmetry doesn't work for generic experiment.
http://physicsworld.com/cws/article/news/45182

kallog, one more thing.
Your mistake is a third newtons law consequence of modern classical mechanics where translational momentum must be equal. For simple form where objects have same translational motion - yes.
However in our case it doesn't work.
Ok. Let's imagine simples case where objects are rolling on one side only. Let's assume the translational momentums for our case equal. Then, forces which induce translational motion must be equal too. But which force induce rotational motion? Yes, the objects rotation in both direction are equal. But what force? We don't any spring inside subset of rolling objects. Just weightless platform between them.

Repulsion objects using laser.
http://knol.google.com/k/paradox-of-classical-mechanics-2#Repulsion_objects_using_laser(2E)

All explanation of this effect has a little problem. The spring should have very little weight.The ideal spring may have mass zero, but it's just an ideal model Is it possible make the spring is weightless on real world?
The answer is - YES. it just need replace mechanic spring by photons. The photons have and impulse, however the stationary mass of them is zero.
This diagram shows this repulsion using laser ray.

The laser itself has two rays with same intensive in opposite detections to each other. The net momentum for for laser is equal zero. However, these rays hit two cylinders with different alignment relatively to rays position.
Is it was described before these cylinders with same mass will have a different translational velocities.

This article came form this site
http://knol.google.com/k/alex-belov/repulsing-objects-by-photons/1xmqm1l0s4ys/23#

Repulsing objects by photons

Base radiation pressure or light pressure phenomenon, the the particle photon with stationary mass zero has a momentum which can be transfered to an object. The good example is a light mill.
The light radiation and objects repulsion must be follow by law of momentum conservation. The figure1 shows repulsing two identical objects with mass m. After a period of time the objects are utilizing photons momentums and start conduct a translational motion. If laser system has identical ray intensity in both directions then objects will have translational momentums P with same value.

Other words, the objects with same mass m will have same velocities v1.

The laser system with identical ray intensity in both directions has zero net momentum.

However, the objects will utilize less photon momentums when these objects increase it's own velocities relatively to laser. The speed of light is constant. However, base on Doppler effect the photons will increase wavelength which reduce photons momentum.


Other words, the objects linear velocities will gain in non-linear mode.

How photons will repulse objects if one of them is rotating?
The figure2 shows repulsing objects by photons where one of them conducts rotation around it's own center of mass.



In this case, this objects will utilize photon momentum differently. After some period of time, the non-rotated object will utilize photons momentums on velocity v. However, the rotated object will utilize photons momentums on velocity v+wR. Base on Doppler effect the rotated object will utilize photons momentums less then non-rotated object. Therefore, after some period of time the rotated and non-rotated objects will have different translational velocities v1 and v2.

Will it work into air environment ?
The goal of this article is transfer translational momentum without mass transfer. Would it possible to do it into air environment? What if transfer momentums to objects through air wave? The Doppler effect for rotated object will be a plus.


Conclusion
Base on Doppler effect and particles(photons) with zero stationary mass, the repulsed objects may have different translational velocities by value inside isolated system.

http://knol.google.com/k/alex-belov/the-concept-of-wave-propulsion-system/1xmqm1l0s4ys/24#

This propulsion concept use ideal models like:
1. The wave source produce pure directional waves which transfer momentum only in particular direction.
2. The wave receivers completely utilize directional wave and don't reflect secondary waves back.
3. The known wave which can transfer momentum without mass - photon.

The figure1 shows first concept of wave propulsion system.



The wave doesn't transfer mass. However, the wave may transfer momentum. Base on Doppler effect, the rotated wave receivers utilize waves with different wavelength. Base on this wavelength difference the receivers will utilize momentum of wave with different values. This momentum difference let system move in particular direction.

The figure 2 shows second concept of wave propulsion system.



Here's wave path through a curve channel and hits wave receivers into one direction.
The utilized by receivers momentums of waves let system moves into particular direction.

One more time.
http://knol.google.com/k/alex-belov/the-wheels/1xmqm1l0s4ys/18#
Base on trivial case of problem, the figure 4 shows a model for experiment where wheels and solid block covers by another platforms on wheels.


The wheel1_1 and wheel1_2 connect with cover by axis.
For easies calculation, all doted elements, platforms and spring are weightless.

Let's assume the law of momentum conservation always works in simplest form. In this case, the forces on both sides of spring are equal by value and induce translational motions for solid block and rolling objects on both platforms. However, which force induce rotational motion for rolling objects on one platform? The solid block doesn't conduct rotational motion on other platform. On one platform, the rolling objects rotate on opposite direction for each other and have same angular momentum by value and opposite direction. However, need a force to induce this rotation. The asymmetrical force cannot exist during interaction. Therefore, the assumption where law of momentum conservation exist in simple form during complex interaction is wrong.

Back to original problem.
The Noether's theorem talks about symmetrical interaction.
Is this action symmetrical or asymmetrical?
http://knol.google.com/k/paradox-of-classical-mechanics-2#

You don't show that the force must be asymetrical. It isn't. But the energy transmitted by the force is assymetrical.

The asymmetrical force is presenting on physics problem solution.
Anyway.

The experiment for this physics problem:
http://knol.google.com/k/alex-belov/the-wheels/1xmqm1l0s4ys/18#The_Experiment






The video
http://www.youtube.com/watch?v=FjYsQnaocws&feature=player_embedded

If the carts are getting different momentums, as they appear to be, then they must be experiencing different impulses. That's in contrast to your idealized diagram where the impulses would be the same.

Can you explain how the spring works. It doesn't look anything like the diagram. The high speed parts are a concern because they'll carry a lot of momentum that's assumed to be zero in the diagram.

Could you look into problem solution, please.
http://knol.google.com/k/alex-belov/the-wheels/1xmqm1l0s4ys/18#
"Let's assume the law of momentum conservation always works in simplest form. In this case, the forces on both sides of spring are equal by value and induce translational motions for solid block and rolling objects on both platforms. However, which force induce rotational motion for rolling objects on one platform? The solid block doesn't conduct rotational motion on other platform. On one platform, the rolling objects rotate on opposite direction for each other and have same angular momentum by value and opposite direction. However, need a force to induce this rotation. The asymmetrical force cannot exist during interaction. Therefore, the assumption where law of momentum conservation exist in simple form during complex interaction is wrong."


Actually same. The one cart repulses form another through spring. It does not what spring shape is. The spring must have same forces on both sides on ideal model.
==
BTW.
This is the force resistance test.
http://www.youtube.com/watch?v=AsQ9GsRThwQ&feature=player_embedded
If you see there both carts mostly have same distance.

I see. Yea I realized afterwards that it doesn't matter about the details of the spring.

Still, you need to determine errors and control for factors that might make it unfair. For example friction. I know the friction seems low, but the friction of a swivelling office chair also seems low, yet you can propel or rotate yourself on it without pushing against the desk.

You seem to be confusing force with energy. The cart with the wheels receives more energy. It ends up with translational as well as rotational energy. But it doesn't receive more force or more implulse - those must be the same, as you said.

How can you have more energy with the same force and impulse? W=Fd. The cart with wheels has the force applied over a greater distance. That give it more energy with the same force.

I wish you could be clearer on what exactly you think is wrong. Do you mean the law of translational momentum conservation is wrong? Is it an internal contradiction, or disagreement with experiment? Don't say both. We only need to focus on one.

The carts path length difference is about 6 inches (~15centimeters) with full path length 7 and 13 inches. Do you really think the standard deviation can cover this?


Again, the kinetic energy of object is result of work which force do for particular object. The force for one object do whole work just for translational motion. However, the force for another object do work for rotational and translational motions. Base on 3-rd Newtons law force for translational motion of one object is equal to net force for translational and rotational motions of other object. This is what is showing on experiment. The force is equal to net(sum) force. However, the forces for translational motions of these carts are not equal.

This is a good question. Do you realize one of the object just move, but on another cart moves and flywheels rotate on it. What force is rotating these flywheels? Where energy came from?


I mean the simple trivial consequence from 3-rd Newtons law as law of momentum conservation in simple form doesn't cover a complex objects interaction. The experiment shows that. The carts with same mass can have different translational momentums after asymmetrical repulsing action.

I added an experiment2 into my site.
http://knol.google.com/k/alex-belov/the-wheels/1xmqm1l0s4ys/18#The_Experiment_2
The result shows something. What is something? It's a big question

Hello ABV, I missed your replies so I'm a bit slow sorry.



It may not be a random error. Can you reduce friction and see if the difference becomes less? Or even easier, increase friction and see if it becomes more. You're saying it should remain unchanged with small changes in friction.


Yes. A single force can be applied to several different things which all receive the entire force.


Yes, but the total force isn't the sum of the forces for translational and rotational motions. All 3 forces are the same (or rotational can be a bit less due to imperfections).


Again you're confusing force with energy. Two identical forces can transfer different amounts of energy. Work=force*distance. You can change distance to get different amounts of work (energy) from the same force. This is what you're doing.