Violation of conservation of angular momentum

[eosphorus]

if i have 1kg mass spinning around an axe with a radius of 100 m and i reduce the radius to 1 m what will be the linear velocity of the 1kg mass?

if you say it will be 100 m/s what happens in the case of a tetherball that varies from a radius of 100m to a radius of 1 m without applying energy to the system, wouldn't conservation of energy be violated because the 1kg mass goes from a speed of 1 m/s to one of 100m/s without applying energy to the system?

and if you say the speed remains constant of 1 m/s however the radius wouldn't be conservation of momentum be violated?

any help?

 

[ZapperZ]

There is a very long and involved thread on the tetherball already that can be found here:

https://www.physicsforums.com/showthread.php?t=66697&highlight=tether+ball

The issue boils down to the ratio of the radius that the ball is rotating versus the radius of the "pole". At some point, the non-central force will no longer conserve the angular momentum.

Zz.

 

[jtbell]

wouldnt conservation of energy be violated because the 1kg mass goes from a speed of 1 m/s to one of 100m/s without applying energy to the system?

Imagine you're holding the cord and the ball is revolving around you. In order to shorten the radius from 100m to 1m, you have to pull on the cord, and do work, which increases the kinetic energy of the ball.

Now I'll anticipate the next question. "But the force is radially inward and the ball is moving tangentially at right angles to the radius. How can the force transmitted via the cord do work on the ball?"

The answer to that question is that while you're pulling the ball inwards, it isn't moving in a circle at right angles to the cord. It's moving in an inward spiral, and the direction of motion has a component along the radius. So $\vec F \cdot d \vec s$ is not zero.

 

[Doc Al]

If you read the thread that ZapperZ referenced, you'll see that the tension in the cord does no work on the ball.

 

[pervect]

The tetherball thread was very interesting, I must have missed it somehow before. Anyway, someone actually writes down the Lagrangian for the tetherball in the thread. I agree with Doc Al and Zapperz that, assuming a massless string, the kinetic energy of the ball should be conserved, and that the angular momentum of the ball around the pole should not be conserved.

Of course angular momentum as a whole is conserved, because the pole is rigidly attached to the Earth - when I say that angular momentum isn't consesrved, what I really mean is that the ball is transfering angular momentum to the Earth via the pole.

 

[eosphorus]

after reading the thread i understand that the law of conservation of angular momentum is not valid in a tetherball nor in any gearing that pulls or let's away the cable giving no energy to the system

so the conservation of angular momentum is false in the case you keep the energy of the system and it only acomplishes in the case you apport extra energy in favour or the system or against it

then why I am taught that conservation of angular momentum always acomplish when even physicists say it doesn't accomplish for whatever reason in a tetherball

will ever be solved this mistake in textbooks?

or is it that conservation of momentum doesn't acomplish in a tetherball or any mechanism similar that doesn't apport any energy but like textbooks teach it must always acomplish...

im sick of hearing that conservation of angular momentum is one of the most experimented and confirmed physical principles in nature when there's an obvious example that violates this principle

 

[ZapperZ]

after reading the thread i understand that the law of conservation of angular momentum is not valid in a tetherball nor in any gearing that pulls or let's away the cable giving no energy to the system

so the conservation of angular momentum is false in the case you keep the energy of the system and it only acomplishes in the case you apport extra energy in favour or the system or against it

then why I am taught that conservation of angular momentum always acomplish when even physicists say it doesn't accomplish for whatever reason in a tetherball

will ever be solved this mistake in textbooks?

or is it that conservation of momentum doesn't acomplish in a tetherball or any mechanism similar that doesn't apport any energy but like textbooks teach it must always acomplish...

im sick of hearing that conservation of angular momentum is one of the most experimented and confirmed physical principles in nature when there's an obvious example that violates this principle

But, but it IS under the condition which the conservation laws apply!

Classical, angular momentum of the UNIVERSE is conserved. Your tetherball is attached to ANOTHER system, i.e. the pole, that eventually will NOT produce a purely CENTRAL force. That whole thread dealt with this issue. ANY system, not just the tether ball, whereby there is an EXTERNAL torque (i.e. a force that isn't radial to a circular motion) will NOT conserve the angular momentum of that system. However, if you consider the tetherball, the pole, the Earth that the pole is attached to, the weak gravitational coupling between the Earth and the sun, the Earth and the moon, etc.. then YES, angular momentum of that WHOLE system is conserved!

Zz.

 

[eosphorus]

"Of course angular momentum as a whole is conserved, because the pole is rigidly attached to the Earth - when I say that angular momentum isn't consesrved, what I really mean is that the ball is transfering angular momentum to the Earth via the pole."

what if i put in the pole a cspinning chair put a weight in my extended arm and then retarct it i suppose then that the weight doesn't increase its velocity just like a tetherball because it trnsfer its momentum to the earth

its exactly the same but just doesn't happen; why because conservation of momentum fails in atetherball

why would i transfer part of the momentum in the case of the tetherball to the Earth and not in the case i retract my arm with the spinning weight?

 

[ZapperZ]

"Of course angular momentum as a whole is conserved, because the pole is rigidly attached to the Earth - when I say that angular momentum isn't consesrved, what I really mean is that the ball is transfering angular momentum to the Earth via the pole."

what if i put in the pole a cspinning chair put a weight in my extended arm and then retarct it i suppose then that the weight doesn't increase its velocity just like a tetherball because it trnsfer its momentum to the earth

its exactly the same but just doesn't happen; why because conservation of momentum fails in atetherball

why would i transfer part of the momentum in the case of the tetherball to the Earth and not in the case i retract my arm with the spinning weight?

You are forgetting Newton's 3rd law, which also applies not only to a linear force, but also to torques. When you try force something to spin, you apply a torque. If you are floating in space with no available friction, do you think doing this will be as easy? Those astronauts who have to fix stuff in space realize very quickly that when they have to turn a screw, they'd better hang on to something else at the same time because if not, they will be the one turning, not the screw.

When there is a NON-RADIAL force being applied to a rotational motion, it means that there is a net torque in the direction of motion. Look again at a plane polar coordinate system. Any non-radial vector will imply a non-zero TANGENTIAL component. This is the torque!

When you pull your arms in, you assume that you are pulling it radially, and you are also on a frictionless surface. So where is the NET non-radial component of the force pulling your arms in? The most common treatement of such a thing is a purely radial force exerted by your muscles to pull your arms in. Furthermore, there's nothing external being exerted to your system (i.e. you spinning), unless you start including friction. This is DIFFERENT than the tetherball system where the pole interacts with the ball. If the radius of the pole is significant enough that the component of the non-radial force becomes a factor, then the tetherball (and ONLY the tetherball) will feel a tangential force.

Zz.

 

[eosphorus]

i have a 4kg pole floating in empty space there are 4 tetherballs attached to it one pointing at 12 oclock ,the others at 3, 6 and 9. the balls at 12 and 6 go clockwise and the balls at 3 and 9 counterclock wise

the momentum transferred to the pole nullify each other so no momentum is transmitted to the floating pole so to keep truth the conservation of angular momentum the balls should speed up as they get close to the center, but that just doesn't happen

do you like the emperors new dress? do you? well I am afraid he is naked

 

[ZapperZ]

i have a 4kg pole floating in empty space there are 4 tetherballs attached to it one pointing at 12 oclock ,the others at 3, 6 and 9. the balls at 12 and 6 go clockwise and the balls at 3 and 9 counterclock wise

the momentum transferred to the pole nullify each other so no momentum is transmitted to the floating pole so to keep truth the conservation of angular momentum the balls should speed up as they get close to the center, but that just doesn't happen

do you like the emperors new dress? do you? well I am afraid he is naked

I dare you to make the tetherball wrap around that pole in THAT situation. How do you propose to supply a "central force" of any kind there?

Conservation laws are based on underlying symmetry principles. What you have dismissed is based on one of the most intrinsic property of our empty space. The conservation of angular momentum is as fundamental as the conservation of linear momentum and the conservation of mass/energy. Via the Noether theorem, the ISOTROPIC nature of our empty space is the very reason why there is a conservation of angular momentum.

If you do not believe in the conservation of angular momentum, I strongly suggest you do not risk your life using it by flying in any airplane. They all use gyroscopes!

Zz.

 

[eosphorus]

all right i hadnt got it before the thickness of the pole causes torque on earth, i can agree with that

but i can easily make a mechanism that pulls radially by means of gearing

it spins and the gearing transforms the spin into pull or letting away

its exactly the same that the tetherball but being the pull totally radial so no torque appears there?

so if i decrease the radius from 100 m to 1 m by means of gearing that pulls radially are you suggesting that the speed should go from 1 to 100 m/s?

then what energy has increased the linear speed if there's only gearing no extra energy aportation?

if not what happens with conservation of momentum because as i said being the pulling radial there's no torque to tranfer to earth, where did the momentum go because it is not transferred to the Earth being the pull radial?

 

[eosphorus]

"I dare you to make the tetherball wrap around that pole in THAT situation. How do you propose to supply a "central force" of any kind there?"

the 6 ball will hold the 12 ball and the 3 ball will hold the 9 ball and since they wind at the same rate they hold on each other all the time and the torque produce by the counterclock wise 12 and 6 balls is balanced by the clockwise 3 and 9

by the way what does isotropic mean?

 

[ZapperZ]

all right i hadnt got it before the thickness of the pole causes torque on earth, i can agree with that

but i can easily make a mechanism that pulls radially by means of gearing

it spins and the gearing transforms the spin into pull or letting away

its exactly the same that the tetherball but being the pull totally radial so no torque appears there?

so if i decrease the radius from 100 m to 1 m by means of gearing that pulls radially are you suggesting that the speed should go from 1 to 100 m/s?

then what energy has increased the linear speed if there's only gearing no extra energy aportation?

if not what happens with conservation of momentum because as i said being the pulling radial there's no torque to tranfer to earth, where did the momentum go because it is not transferred to the Earth being the pull radial?

I don't get it. Are you asking for ANY example that has a demonstration of conservation of angular momentum, or are you still working on this tetherball problem? I thought the tetherball problem has been sufficiently explained?

I put you in space with ZERO interaction of any kind with anything external. You are already spinning. You pull your arms in. No other external force acts on you. No matter what you do (pull your legs in, stick your tongue out, push your elbow in), your angular momentum will always be conserved no matter how your moment of inertial changes.

Zz.

 

[ZapperZ]

"I dare you to make the tetherball wrap around that pole in THAT situation. How do you propose to supply a "central force" of any kind there?"

the 6 ball will hold the 12 ball and the 3 ball will hold the 9 ball and since they wind at the same rate they hold on each other all the time and the torque produce by the counterclock wise 12 and 6 balls is balanced by the clockwise 3 and 9

by the way what does isotropic mean?

Oy vey! That's it, I'm done.

Zz.

 

[eosphorus]

i have an example in which no momentum is transferred to earth, just a double counterrotatory tetherball the torque in on sense is compensated by the torque in the other sense so the torque transmitted to Earth is 0

then in a double tetherball not being transference of momentum to Earth the linear velocity should increase as the radius decreases as conservation of angular momentum states but I am afraid linear speed would remain constant

 

[Doc Al]

i have an example in which no momentum is transferred to earth, just a double counterrotatory tetherball the torque in on sense is compensated by the torque in the other sense so the torque transmitted to Earth is 0

then in a double tetherball not being transference of momentum to Earth the linear velocity should increase as the radius decreases as conservation of angular momentum states but I am afraid linear speed would remain constant

Nope. Just because the total angular momentum is zero doesn't mean that the angular momentum of each tetherball is conserved. There's still torque on each tetherball.

 

[pervect]

i have a 4kg pole floating in empty space there are 4 tetherballs attached to it one pointing at 12 oclock ,the others at 3, 6 and 9. the balls at 12 and 6 go clockwise and the balls at 3 and 9 counterclock wise

the momentum transferred to the pole nullify each other so no momentum is transmitted to the floating pole so to keep truth the conservation of angular momentum the balls should speed up as they get close to the center, but that just doesn't happen

do you like the emperors new dress? do you? well I am afraid he is naked

It's rather hard to tell your physics level, though this last comment about "emperors" makes me revise it downwards rather sharply :-(. Snippy comments plus a lack of equations plus an intuitive leap to a false conclusion that physics is at fault (rather than your understanding of the problem) is just not a good sign :-(. Ah well, perhaps you are simply young and immature, and there's definitely a very slim chance that you'll learn something about physics from this thread. And if you refuse to learn, at least you have presented a somewhat interesting problem that's entertained the rest of us for 5 minutes or so.

The answer to your restated problem is quite simple, though.

The motion of anyone of the individual balls is the same as it is in the first problem - it conserves energy.

But what about the angular momentum of the system, you ask, politely. (OK, I just threw that part about being polite in there, it wouldn't surprise me terribly if you turn out to be rude). Well, it's obvious isn't it?

No?

Think...

Think a little more.

What is the numerical value of the angular momentum of the system? It's zero! It's zero because for every ball roatating clockwise, you have one rotating anti-clockwise.

Now, what is the angular momentum of the system after the balls have "wound in" in such a manner that each ball individually conserves its energy?

It's STILL ZERO! By symmetry!

Thus the system conserves both angular momentum (which is always zero, by symmetry) and energy. This is what one would expect from an isolated system.

 

[eosphorus]

according conservation of angular momentum if the tetherballs don't increase its linear speed decreasing the radius as planets do that angular momentum must be transferred somewhere or converted to heat, noise, light, pressure,etc but in the case of a frictionless example this won't happen so the tetherballs will rebound wrapping and unwrapping and so on forever at a constant linear speed

you state that the counter rotating tetherballs would be giving angular momentum to Earth when winding and taking it from Earth when unwinding
so angular momentum as a whole would be conserved

but in the case of a double frictionles tetherball at no time angular momentum would be tranferred to Earth and the energy wouldn't be dissipated the tetherballs would rebound, then the angular momentum would decrease when winding and increasing when unwinding

of course I am an ignorant about physics, in fact i haven't even passed my physics course in college but I've spent thousands of hours trying to understand nature and say what i see that happens

 

[eosphorus]

in the clasical example when you would be pulling and unpulling as planets do gravity doesn create energy there's just a transformation of potential energy into speed and viceversa

the problem of the double tetherball is that it just doesn't behave intechanging kinetic energy for potential energy

it creates potential energy

 

[ZapperZ]

according conservation of angular momentum if the tetherballs don't increase its linear speed decreasing the radius as planets do that angular momentum must be transferred somewhere or converted to heat, noise, light, pressure,etc but in the case of a frictionless example this won't happen so the tetherballs will rebound wrapping and unwrapping and so on forever at a constant linear speed

you state that the counter rotating tetherballs would be giving angular momentum to Earth when winding and taking it from Earth when unwinding
so angular momentum as a whole would be conserved

but in the case of a double frictionles tetherball at no time angular momentum would be tranferred to Earth and the energy wouldn't be dissipated the tetherballs would rebound, then the angular momentum would decrease when winding and increasing when unwinding

of course I am an ignorant about physics, in fact i haven't even passed my physics course in college but I've spent thousands of hours trying to understand nature and say what i see that happens

Then may I suggest that you SHOULDN'T be quick at making insulting remarks such as "...do you like the emperors new dress? do you? well I am afraid he is naked..." It is insulting to people who is in this profession by implying that all of us do nothing but follow things blindly.

Secondly, the things that you "see" are not something done under the strictest experimental conditions. How do you know what you saw cannot be explained by other means? Are these done very carefully to isolate what is being studied from being influenced by other factors? I'm an experimentalist, and it is MY JOB to perform tests and measurements, and I am always conscious of factors that can influence my measurements. Are you CERTAIN that you have made a careful-enough measurement that allows you to make such blatant statements?

There is a difference between asking questions because one doesn't understand, and coming in here with already a fixed attitude that "basic physics" is wrong. I am willing to spend a lot of time dealing with the former, but I have no patience nor desire to entertain the latter.

Zz.

 

[eosphorus]

i apologize if i was ofensive it was not my intention but let's discuss the case of the tetherball youll see I am right:

i have an isloated system of two masses of 1 kg each they got an angular momentum with respect to each other of 1, i unite them by a cable so it winds inwards,then it rebounds and reaches initial position but going outwards this time

let the distance among them now grow to infinity the angular moment with respect to each other now will be infinite because the distance is infinite and the linear relative speed keeps constant

angular momentum with respect to each other goes from 1 to infinite if you have infinite cable because the linear speed will be constant

the relative linear speed of the balls remains constant but the distance grows to infinity growing the angular momentum from the initail to infinitum

in an outwards tetherball there's creation of angular momentum from a given relative angular momentum, you can create as much momentum as cable you have

 

[eosphorus]

lets take the Earth example i start the tetherball with 1 kg mass ball 1 m radius and 1 m/s speed the theterball winds and transfers its angular momentum to earth, when it rebounds the tetherball momentum is 0 but while unwinding recovers that lost momentum, now the Earth doesn't have any of the initial momentum when its again in the initial position

but now an opposite momentum to the tetherball is acting on Earth because of the thickness of the pole and the theterball linear speed remains constant

the linear speed of the tetherball remains constant so the angular momentum of the ball increases with the radius and the opposite momentum of the Earth could reach infinity if you let the radius grow to infinity

 

[ZapperZ]

i have an isloated system of two masses of 1 kg each they got an angular momentum with respect to each other of 1, i unite them by a cable so it winds inwards,then it rebounds and reaches initial position but going outwards this time

Back up! Why would this "rebound" occur? There's nothing to reverse the angular momentum of each of the two balls, which is what would occur of they start to unwind. Have you seen such a thing happening?

Zz.

 

[eosphorus]

all right ill change my question:

i have a tetherball that can unwind to the infinity

i give a initial angular momentum to the thetherball of 1

seems agreed by everybody here that the linear speed of the tetherball will keep to infinitum

the initial angular momentum of the Earth is 0

the theter unwinds clockwise to infinitum at a constant linear speed

the thickness of the pole exerces a torque which causes Earth to acquire an angular momentun conterclockwise

being the torque kept ad infinitum the Earth acquires infinitum angular momentum counterclockwise

now we have a counterclockwise infinite torque on Earth and infinitum angular momentum on the tetherball with respect to the Earth on the other sense

of course they together add an angular momentum of 0 but well let's just throw the tetherball to meet the universe and let us keep the infinite torque acquired by earth

i just don't get where this energy has come from

 

[ZapperZ]

all right ill change my question:

i have a tetherball that can unwind to the infinity

i give a initial angular momentum to the thetherball of 1

seems agreed by everybody here that the linear speed of the tetherball will keep to infinitum

the initial angular momentum of the Earth is 0

the theter unwinds clockwise to infinitum at a constant linear speed

the thickness of the pole exerces a torque which causes Earth to acquire an angular momentun conterclockwise

being the torque kept ad infinitum the Earth acquires infinitum angular momentum counterclockwise

now we have a counterclockwise infinite torque on Earth and infinitum angular momentum on the tetherball with respect to the Earth on the other sense

of course they together add an angular momentum of 0 but well let's just throw the tetherball to meet the universe and let us keep the infinite torque acquired by earth

i just don't get where this energy has come from

Huh?

Do you realize that you KEEP CHANGING the situation almost on every posts that you have made? First it was just a simple tetherball, then it became a tetherball in space, then there's TWO tetherball in space, and now a tetherball at infinity...

Here's a question for you. When you pull your arms in while spinning on ice, your angular momentum remains constant, but your ROTATIONAL KINETIC ENERGY does not! Where do you think this energy comes from?

Zz.

 

[Pyro]

all right ill change my question

The conservation of angular momentum doesn't care how you change the question. The conservation will always hold.

 

[Danger]

Is it premature of me to say "Hi, Aviator?":uhh:

 

[ZapperZ]

Is it premature of me to say "Hi, Aviator?":uhh:

Nope.. because I felt it early last night already.

:)

Zz.

 

[eosphorus]

i change the example because somebody proves it wrong like in the rebounding tetherball where it wouldn't rebound

but what happens in my last example

everybody agrees that the linear speed remains constant however the radius of the tetherball and that a torque is exerted on Earth because of the thickness of the pole

i just reach the obvious conclusion that there's a creation of kinetic energy without apporting energy because the Earth gets infinite torque from an initial angular momentum in an expanding tetherball

saying that conservation of energy and angular momentum can't be wrong is not an argument, discuss my point

as for the increase of kinetic energy in the case of the ice skater it comes from food

 

[Doc Al]

It's difficult to follow your example. Please restate it without any wildly unphysical "infinities". Where do you see energy being created? (Note that in a real tetherball case there is gravity pulling the ball down.)

 

[Haelfix]

Conservation of angular momentum is a mathematical theorem, its simply unavoidable. Its proved in any number of ways in most elementary books on mechanics. Try as you like to find a counter example, and they can get arbitrarily complicated, you won't succeed without making a mistake (and sometimes the mistake can be made arbitrarily subtle).

 

[pallidin]

I have read this thread with great interest, as well as the link to another thread given at the beginning. I have a question:

If the tether ball is released from the string just before it's spiral motion impacts the pole, would it travel farther than is accounted for from the initial impact force of hitting the ball it the first place?
Hope my question makes any sense.

 

[pallidin]

If I am understanding all of this correctly, there is a net gain in energy, but that the energy source is the torque resistance of planet Earth within that frame of reference.

 

[eosphorus]

"If the tether ball is released from the string just before it's spiral motion impacts the pole, would it travel farther than is accounted for from the initial impact force of hitting the ball it the first place?""

the trick of the tetherball is that the linear speed remains constant however the radius so when it hits or is relesed from the pole the energy is the same either kinetic when released or transformed in heat and noise when hitting


take a tehterball 1kg mass 1 m initial radius 1 million kilometers final radius

take an Earth 1000 tons mass so gravity gets really weak

create amomentum on the tetherball of 1 and the Earth has o momentum of 0

lets suppose a thickness of the pole of 1 m and the thickness of the cable of 0

the tetherball starts to unwind, its been agreed that the tetherball keeps a constant linear velocity however the radius and that a torque is exerced on the pole and transferred to Earth because of its thickness

the linear speed of the ball is the same and there's a constant torque on the earth

the ball gains angular momentum from the Earth because the radius increases from 1 m to 1 million km and the linear speed remains at 1 m/s

the Earth gains torque from 0 to a big number because the radius of the thickness of the pole and the tension of the string have created this torque

both the torque of the Earth and the angular momentum of the Earth will add a total momentum of one the initial one