The Acceleration of the Center of Mass and External Force

[e2m2a]

Suppose I perform an experiment, set up as follows: There is a rotating body which rotates around a vertical axis. The axis is at one end of the rotating body (denoted as the rotator) so that the axis is not through the center of mass of the rotator. The vertical axis is attached to a second body, denoted as the slider. The slider is constrained to move along
a linear track with one degree of freedom. It moves parallel to the x-axis of an x-y coordinate system. At some prior time the center of mass of the rotator-slider system is determined by a balancing measurment, and a red circle is placed on the rotator at the exact center of mass of the rotator-slider system.
Initially, the rotator is parallel to the y-axis or at the "12 o'clock" position. We apply a force in the negative x-direction on the rotator. The slider is in contact with a left bumper, such that it cannot move to the left when the force is applied. After the force or torque is applied through an angular displacement, that is, we do initial work on the rotator, the rotator rotates at a constant angular velocity in the counter-clockwise direction. When the rotator is at the 5 o'clock position, we apply a second short outward radial force on the rotator, being careful that the force is always on the same line that goes through the axis of rotation and the center of mass of the rotator.
While all of this is happening, a high-speed video camera records the motion of the center of mass of the system, (the red circle). Analysis shows that after the initial force on the rotator, the speed of the red circle or the center of mass of the system remains constant until it reaches its 5 o'clock position. However, during the time the second outward radial force is applied, beginning at the 5 o'clock position, the speed of the center of mass increases. And after we stop applying the second force, the high speed video camera reveals that the speed of the center of mass(red circle) is greater than the initial speed of the center of mass. This may seem like a dumb question, but why did the speed of the center of mass of the system increase? And does this imply that the second force did work on the system, increasing its kinetic energy?

 

[zhermes]

Picture?

 

[e2m2a]

I have no picture, but to be honest, I already know the answers to the rhetorical questions. It's obvious. The increase in the speed of the center of mass was due to the second outward radial force that was applied to the rotator. This would cause the rotator-slider system to move to the right with an increase in the speed of the system's center of mass.
This follows from Euler's first law and the conservation of momentum. Since the speed of the center of mass increases, it follows that the kinetic energy of the system increases.
But here is the significant point. I have actually performed an experiment as described in the thought experiment, except I don't apply a second outward radial force to the rotator when it has reached the 5 o'clock position. What is significant about the experiment is that the high-speed video shows the speed of the center of mass of the rotator still increases. The only force acting on the system was an inertial, centrifugal force. That is, inertia alone, did work on the rotator-slider system to increase its kinetic energy. This is incontrovertible because the speed of the center of mass of the system increased.
If you want to see a video of the experiment, send me a message in my personal account, and I will e-mail it to you.

 

[Doc Al]

All this talk of rotors and sliders is very confusing (at least to me) without a detailed diagram of what you are doing.

Are you claiming that you have some device whose center of mass accelerates even though there is no external force acting on it? How have you ensured that no external force, including friction, acts? Is the device a rigid object? If not, how are you measuring the motion of its changing center of mass?

The only force acting on the system was an inertial, centrifugal force.

An odd statement, since centrifugal force is a fictitious force that only appears when analyzing things from a rotating frame. Or do you mean something else?

The vertical axis is attached to a second body, denoted as the slider. The slider is constrained to move along
a linear track with one degree of freedom.

Sounds like external forces are acting to me.

 

[zhermes]

Nope, I think @e2m2a is right. We have free-energy. Its here. He's got it. Proven. DONE! He has a VIDEO! "Next song."

 

[e2m2a]

Doc Al, here is a response to your questions. First of all, I don't know how to post a diagram of the experiment to this forum, but I can send a video of the device in motion. If it is possible, I will post it to this thread. It is in avi format. If you are anyone is interested in seeing the video, you can send me an e-mail if it is permitted by the rules of this forum to give out my e-mail address.

No, I am not claiming that the speed of the center of mass of a system is increasing when there is no external force, acting on the system. This would be impossible for it would violate the conservation of linear momentum and Euler's first law. The system consists of two rigid bodies, one is denoted as the rotator and the other as the slider. The slider essentially can only move in a straight line along a linear path. The rotator rotates around a vertical, physical axis which is connected to the slider. The axis is off center from the center of mass of the rotator.

Friction is existent in this experiment as it is in all experiments. Friction, obviously, has a bearing on the speed of the center of mass of the system, for it decreases the maximum amount of speed possible, but it does not cause the acceleration of the center of mass of the system. Let me draw a crude analogy of how friction acts in this experiment. Suppose there is a body at rest on a linear track. A rope is attached to the body and someone pulls on the rope. Of course, the body will begin to accelerate as soon as the force from the rope overcomes the force due to the coefficient of static friction. During this acceleration, there will be friction forces from the track due to the coefficient of kinetic friction, acting on the body. This friction force will subtract from the force of the rope, decreasing the net acceleration of the center of mass of the body, but clearly, it has no bearing on what is causing the acceleration in the first place. It is the rope that causes the acceleration. In the experiment the slider is constrained to move along a linear "track". Friction from the track affects the net speed of the center of mass, but it plays no part in causing the acceleration as explained in this analogy.

The center of mass of the rotator-slider system was determined by a balancing measurement. We then placed a red circular sticker on the rotator at this center of mass point. The center of mass was used as the basis of our measurement and not the center of mass of the rotator, because the center of mass of a system is a "sifter" of true and false conjectures about the dynamics of a system. For example, uninformed inventors or experimentalists might try to accelerate a system by the action of internal forces to the system. Such an attempt would be hopeless from the start because only an external force, acting on the system, can change the speed of the center of mass of the system. In our experiment we measured an increase in the speed of the center of mass of the rotator-slider system, thus indicating, an external force acted on the system.

We used a high speed video camera, shooting at 210 frames per second, to analyze the motion of the center of mass of the system. Afterwards, an AUTOCAD program was used to analyze the motion of the center of mass, and clearly, it showed the speed increased. During the time the speed of the center of mass increased, there were no applied, physical contact forces acting on the system, other than friction as discussed earlier.
Care was taken so that the rotator-slider system was level so that gravity would not impact the motion of the center of mass.

Although the direction of the center of mass was continuously changing, this did not have any relavance on what we were measuring-- speed. That is, we were not concerned with change in direction because change in direction per se does not mean a change in magnitude. We were only concerned with a measurement in the scalar domain, a measurement of magnitude or speed. An increase in speed means an increase in kinetic energy per the very definition of kinetic energy.

The only force acting on the system during the increase in speed of the center of mass, other than friction, was an inertial force. You are right, I am technically wrong in using the term centrifugal force because by convention this only applies to non-Newtonian fictitious forces measured in a non-inertial frame, such as centrifugal or Coriolis forces. For now, I will just denote it as an outward radial inertial force with respect to an inertial, laboratory frame. For short, I will denote it as the radial force.

Is this radial force "real" with respect to a laboratory frame? If we think of it analogous to the rope that pulls on the body, then yes, it is real. But in reality how would we determine if a "candidate" force is real. This is an issue of causality. I submit by the empirical effects
of a candidate force, we can determine if the force is real or virtual or any other name you want to give it. What would be the empirical effects? I submit measuring the effect it has on the speed of the center of mass of a system. If the speed increases, I think it would fulfill a necessary and sufficient requirement as qualifying as a real force.

Again, if it is permitted and possible, I can either send you a video of the experiment or attach it to this thread. Seeing the video will clearly answer any questions you have about the action of the experiment.

zhermes, I would not be so quick to dismiss the observable facts of this experiment. Yes, I can understand your skepticism, being that inertia is the domain of many "crackpots" and those who are pegged as being out on the fringe, practicing pathological science.
However, consider it is also possible to do a serious investigation of the effects of inertia, using rigorous, time-tested scientific methodology. I do not make any ridiculous claims that violate the known conservation laws, such as those who claim energy being created out of nothing and other vacuous nonsense. I have been wrong in the past on my ideas, and I have been first to publicly admit my error on this forum. However, the empirical data of the experiment justifies a serious inquiry into this pecular efect that can only be
attributed to the effects of inertia. It is a replicable, empirical fact that the speed of the center of mass of the rotator-slider system increases. I am ready to answer any questions about how the measurements were made. I stand on Euler's law and the conservation of linear momentum for an explanation of the results, in that only an external force can cause an increase in the speed of the center of mass. I think, the conservation of linear momentum, being a pillar of physics, is a good place to hang one's hat as far an an explanation is concerned. We wouldn't want to dismiss the conservation of linear momentum, would we?