# If the predictions of physics do not match reality, does the problem lie with reality?

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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.

Closed as per community consensus as the post is not graduate-level
asked Feb 6, 2018 1 flag
recategorized Feb 6, 2018

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.

Falling on the Earth straightforwardly increases the kinetic energy of the falling body. The conserved quantity here is the sum of kinetic and potential energies.

Voting to close.

Actually conservation of angular momentum does not require a closed inertial system. The only requirement is an absence of torque. Since we are talking of adjusting a radius, I am more inclined to think of a tethered object. @annav

@VladimirKalitvianski Are you declaring that angular momentum is not conserved?

I know a lot of people who get very upset with you when you make that declaration. They try very hard to censor any discussion which might suggest that.

The angular momentum conservation may still hold, but what you makes surprised (gain/loss of kinetic energy during interaction) is not surprising at all.

@VladimirKalitvianski You said that the energy was conserved. Now you say that angular momentum is conserved. The simple calculation posted suggests an extreme conflict between the two. I assume that your next claim will be that the energy used to alter the radius makes up the difference. The problem with this claim is that a centripetal force cannot apply a torque which means that it cannot affect the rotational kinetic energy so there remains a conflict between conservation of energy and conservation of angular momentum.

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..

@VladimirKalitvianski, The calculation presented indicates a radius which begins at 1 metre and is reduced to 1 centimetre. A free falling body is not a valid example because it is not orbiting. Centripetal force cannot apply torque. Claiming otherwise is irrational. Otherwise every rotating body would experience constant application of torque because they are constantly experiencing centripetal force. Given your example of the satellite, if you do the calculations you will find that the potential energy variance is far less that the kinetic energy variance predicted if angular momentum is conserved.

PE = mgh so it is directly proportional to h

KE = 0.5 M v^2 and v is indirectly proportional to h (or r) so KE will be indirectly proportional to h^2

Total mechanical energy will not be kept constant if angular momentum is conserved.

I am not confused but it very much appears that you are.

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

This is the third for PO inappropriate high-school level question you have posted on PO. If you keep posting such material, you will be blocked according to our policy. This is your first warning.

Voting to close, 500+ rep users please upvote the closevote here.

@annav, A centripetal force cannot apply a torque and without a torque, we cannot affect the rotational kinetic energy.

@VladimirKalitvianski, I apologise for the original formatting - I could not get the math button to function properly. Inexperience in formatting is not an indication of physics literacy. Your declaration that I am illiterate in physics is straight out ad-hominem. Please cut it out and address the argument.

$PE=m∗g∗h$ so it is directly proportional to $h$

$KE=1/2mv^2$ and if angular momentum is conserved, $v$ (at perihelion and aphelion) is indirectly proportional to $h$ so $KE$ will be indirectly proportional to $h^2$

This means that the total kinetic energy at perihelion will not match that at aphelion if angular momentum is conserved.

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: $h=h(t)$.

This is a classical mechanics problem, please restrict the discussion accordingly?

$KE(rotational) = 1/2Iw^2$

$I=mr^2$

$w=v/r$ (At perihelion and aphelion)

$KE(rotational)=1/2(mr^2)(v/r)^2$

$= 1/2mv^2$

surprising discussion ! let's Dr Mandlbaur take his Nobel and be proud to be members of the recipient he chose for this major contribution to geo dynamics.

Either Mr Mandlbaur does not understand that the rotational KE is not always $1/2 mv^2$, or he is an internet troll. Anyway, I vote to close his question.

A particle swinging over your head on a tether , a string, the force when you pull in the string is not all centripetal as there is an angle. If you have ever done the experiment, you would feel the pull on the string, vertical also, and reducing the string length  would take energy from your hand.

@annav, You cannot possibly account for the difference in energy we are talking about with your straw grabbing nonsense. Wake up and smell the coffee. If you are so convinced I am wrong then produce any evidence to support your claim. There are no experiments which confirm that angular momentum is conserved in a variable radii system. Why is that do you think?

@VladimirKalitvianski, I have made it clear that my argument is regarding the status at perihelion and aphelion of the orbit so your suggestion that I do not understand rotational $KE$ is not always $1/2mv^2$ is nonsense. My argument is valid and you are using ad-hominem to avoid processing it. Grow up and act like a man deserving of his title - assuming you have one. It is you who is trolling here.

@igael, I hope that you are being genuine here. I do not hold the title you have addressed me with but I thank you for the appreciation. It is really great to know that there does exist intelligent life on earth.

@Mandlbaur: You may deal with the equations of motion in polar coordinates or with two conservation laws, whatever. Replace your words with physical quantities and you will see that there is no contradiction between the laws. It's about time to get to it by yourself.

To the other participants: Let us not feed the troll.

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).