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If an orbiting body has it's radius reduced from one metre to one centimetre, conserving angular momentum predicts that the orbital velocity will increase one hundred fold. This of course means that the kinetic energy increases ten thousand fold. Which is an increase to one million percent of original.

Conservation laws hold in closed inertial systems. Think of an orbiting satellite in a stable orbit. To get to a smaller orbit the rockets must supply energy, and in the transition there is an acceleration, and no inertial system. Once in the smaller orbit, the increase in momentum has absorbed the energy given by the rockets.

I do not know exactly what an experimental setup you have in mind, but let us suppose an Earth satellite orbiting our planet in an elliptic orbit. The kinetic energy changes, so does the potential energy, the angular momentum being constant. I do not see any conflict here. I proposed you the simplest case - with a zero (and conserved) angular momentum (a free falling body), but you are still confused.

Concerning your reasoning with the centripetal force, yes, it can change the radial part of the total kinetic energy; thus changing the angular part in the way to keep the total mechanical energy constant.

a"tethered object" : you would have to supply energy to pull in the rotating body, that energy becomes the kinetic energy with the smaller radius tether..

Moderators, WTF??? Close this thread as the PO is illiterate in the elementary Physics.

KE contains the radial part and the angular part. The latter is proportional to a function of radius (or $h$, as you like). So the angular part $\propto \dot{\varphi}$ depends on $h$, and the latter is already determined with the energy conservation equation: $h=h(t)$.

@VladimirKalitvianski,

I am not a scientist. I am not claiming to know more than you about anything. I am not trying to win any prize.

I did some experimentation and discovered that what science taught me is wrong. I do not understand what is happening. I do not have a better theory. I do not intend proposing one.

What I do know is that the ball on a string or the professor on a turntable or the spinning skater or any of the earthly examples and demonstrations given to convince students of conservation of angular momentum do not conserve angular momentum. I measured them.

I also know that there is no variable radii experiment which confirms that angular momentum is conserved. In two years of facing aggressive hostility from people who are clearly upset by the mere suggestion that angular momentum might not be conserved, not a single person has managed to find one. It would have been the simplest way to shut me up.

What I have figured out is that since angular momentum is defined as $L=r \times p$ and $p$ is conserved it is unreasonable to expect that $p$ will effectively abandon that property in order to conserve something else. This appears to me to be the mistake. My experiments also seem to indicate that $p$ is what is being conserved in magnitude.

Every time I have tried to bring this to somebody’s attention I have been insulted and mocked and told I have to get a phD or publish in a peer reviewed journal before anybody will listen.

There is something at a very basic level that is not properly understood by physicists. I feel that it is extremely important that we should understand this properly and that we should not be teaching things that are false to students.

You are the physicists so it seems natural that I should bring it to your attention.

I concluded that the quickest way for me to explain it without wasting time on researching a failed project would be to provide a logical proof.

I have several different logical proofs on my web site.

I have never had a proper review and have defeated all valid objections made to all of them.

@Mandlbaur: The equation of motion for the momentum $\vec{p}$ reads as follows: $\frac{d\vec{p}}{dt}=\vec{F}(\vec{r},t)$, i.e., the momentum is conserved if there is no force. Similarly, the angular momentum is conserved if there is no $\vec{r}\times\vec{F}$, and the total energy is conserved when the potential energy $U(\vec{r})$ does not depend on time $t$ explicitly. This follows from the first equation of motion.

Now you are speaking of some particular experiments. I do not know what you mean. There may be experiments where the momentum is not conserved, or the angular momentum is not conserved, or something else, like an optical illusion or misunderstanding. For example, the angular velocity of a spinning object $\dot{\varphi}$ may increase or decrease, and this can be "understood" as due to angular momentum conservation in an experiment where the angular momentum is actually not conserved. In particular, when a body at one end of a rope rotates around a rod of a finite radius (rolls up) like this:

Then the vector product $\vec{r}\times\vec{F}$ is not zero since the force is not "central", and the angular momentum is not conserved. In such an experiment the conserved quantity may be the absolute value of the momentum $p$ or velocity $v$ (it depends on rigidity of the rope).

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