# Violation of conservation of angular momentum

1. Oct 10, 2005

### 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, 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?

and if you say the speed remains constant of 1 m/s however the radius wouldnt be conservation of momentum be violated?

any help?

2. Oct 10, 2005

### ZapperZ

Staff Emeritus
3. Oct 10, 2005

### Staff: Mentor

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.

4. Oct 10, 2005

### Staff: Mentor

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

5. Oct 10, 2005

### pervect

Staff Emeritus
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.

Last edited: Oct 10, 2005
6. Oct 10, 2005

### 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 lets 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 sytem or against it

then why im taught that conservation of angular momentum always acomplish when even physicists say it doesnt accomplish for whatever reason in a tetherball

will ever be solved this mistake in text books?

or is it that conservation of momentum doesnt acomplish in a tetherball or any mechanism similar that doesnt apport any energy but like text books 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 theres an obvious example that violates this principle

7. Oct 10, 2005

### ZapperZ

Staff Emeritus
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.

8. Oct 10, 2005

### 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 doesnt increase its velocity just like a tetherball because it trnsfer its momentum to the earth

its exactly the same but just doesnt 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?

9. Oct 10, 2005

### ZapperZ

Staff Emeritus
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.

10. Oct 10, 2005

### 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 transfered 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 doesnt happen

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

11. Oct 10, 2005

### ZapperZ

Staff Emeritus
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.

12. Oct 10, 2005

### 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 theres only gearing no extra energy aportation?

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

13. Oct 10, 2005

### 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?

14. Oct 10, 2005

### ZapperZ

Staff Emeritus
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.

15. Oct 10, 2005

### ZapperZ

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

Zz.

16. Oct 10, 2005

### 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 im afraid linear speed would remain constant

17. Oct 10, 2005

### Staff: Mentor

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.

18. Oct 11, 2005

### pervect

Staff Emeritus
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 motion of any one 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.

19. Oct 11, 2005

### eosphorus

according conservation of angular momentum if the tetherballs dont 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 wont 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 wouldnt be disipated the tetherballs would rebound, then the angular momentum would decrease when winding and increasing when unwinding

of course im an ignorant about physics, in fact i havent even passed my physics course in college but ive spent thousands of hours trying to understand nature and say what i see that happens

20. Oct 11, 2005

### eosphorus

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

the problem of the double tetherball is that it just doesnt behave intechanging kinetic energy for potential energy

it creates potential energy