A Problem

[hansda]

This problem just came to my mind. I am wondering, what could be its solution. Here it is:

Consider an isolated system. So there is no energy transfer from/to this system to/from outside.

There is an observer with n identical balls with him in this system. Consider n>2. Initially these balls are at rest with relative to the observer. Now the observer applies some force to these balls. All these balls are spinning. Consider the conservation of angular momentum. These balls will spin in such a fashion, that their angular momentum is conserved.

After some time, the observer holds one ball and stopped its spin. Will it change the spin of other (n-1) balls, so that their angular momentum is conserved?

 

[origin]

This problem just came to my mind. I am wondering, what could be its solution. Here it is:

Consider an isolated system. So there is no energy transfer from/to this system to/from outside.

There is an observer with n identical balls with him in this system. Consider n>2. Initially these balls are at rest with relative to the observer. Now the observer applies some force to these balls. All these balls are spinning. Consider the conservation of angular momentum. These balls will spin in such a fashion, that their angular momentum is conserved.

After some time, the observer holds one ball and stopped its spin. Will it change the spin of other (n-1) balls, so that their angular momentum is conserved?

No. The angular momentum of the single ball will be transfered to the dude that stopped the ball. Stopping one ball will have no effect on the other balls - angular momentum is conserved for the dude/ball interaction and the system.

 

[sideshowbob]

After some time, the observer holds one ball and stopped its spin. Will it change the spin of other (n-1) balls, so that their angular momentum is conserved?

The ball can only transfer its momentum to something it interacts with.

 

[hansda]

No. The angular momentum of the single ball will be transfered to the dude that stopped the ball.

You are considering an isolated system or an open system like our earth? In this isolated system there is no external gravity. All the gravity or spacetime is due to the presence of the n balls and the observer.

Our universe also can be considered as an isolated system, because energy of our universe is conserved/constant. Isn't the angular momentum of our universe is also conserved?

Stopping one ball will have no effect on the other balls - angular momentum is conserved for the dude/ball interaction and the system.

Here the system is consisting of n balls or (n-1) balls?

 

[Sarkus]

You are considering an isolated system or an open system like our earth? In this isolated system there is no external gravity. All the gravity or spacetime is due to the presence of the n balls and the observer.

He didn't mention gravity. The system is the balls and the observer. If the observer interacts with the balls then he is, by definition, part of the system. As others have explained to you, in stopping one of the balls the angular momentum is conserved between the observer and the ball the observer stops. The other balls remain unaffected.

Our universe also can be considered as an isolated system, because energy of our universe is conserved/constant. Isn't the angular momentum of our universe is also conserved?

The angular momentum within our universe is conserved, yes. And most likely is a sum-zero affair - i.e. there is at any given point in time a net zero angular momentum within the universe. But I am not sure of this.

Here the system is consisting of n balls or (n-1) balls?

n balls PLUS the observer. But when the observer interacts with one of the balls, and neither is also acting in any way with anything else, then they also form a system that will conserve energy, angular momentum etc. This smaller system operates within the larger system. If the smaller system conserves these properties then, by definition, the larger system also does (while the items not within the smaller system remain unaffected by anything).

 

[hansda]

He didn't mention gravity.

Thats true. I only mentioned gravity, because through gravity a mass can interact with other mass; be it Newtonian gravity or GR.

The system is the balls and the observer. If the observer interacts with the balls then he is, by definition, part of the system.

In the OP i already mentioned this.

As others have explained to you, in stopping one of the balls the angular momentum is conserved between the observer and the ball the observer stops.

When the spinning ball is stopped by the observer, its kinetic energy may be converted into potential energy. How its angular momentum is conserved? Is it absorbed by the atomic particles or photons?

The other balls remain unaffected.

Not very correct. In Newtonian Gravity, this may be correct but in GR this may not be correct. In Newtonian Gravity spin does not play any role in gravity but in GR spin may cause additional curvature to spacetime causing Frame-Dragging effect. In Newtonian Gravity, there may be an effect of precession also, causing a little change in the angular momentums.

The angular momentum within our universe is conserved, yes.

YES, I also think so.

And most likely is a sum-zero affair - i.e. there is at any given point in time a net zero angular momentum within the universe. But I am not sure of this.

Whatever the angular momentum, at the time of Big-Bang; Say it is conserved at every moment of time. So, it is the same angular momentum now.

n balls PLUS the observer. But when the observer interacts with one of the balls, and neither is also acting in any way with anything else, then they also form a system that will conserve energy, angular momentum etc.

What kind of interaction, you are considering here?

This smaller system operates within the larger system.

The smaller system(as defined by you as the interaction of observer with one of the balls) also can interact with larger system through gravity.

If the smaller system conserves these properties then, by definition, the larger system also does (while the items not within the smaller system remain unaffected by anything).

I think you are not considering the interaction through gravity or effect of precession or effect of Frame-Dragging here.

For a better visualization of this problem, consider an isolated solar system with n identical planets spinning around their centre of mass. Additionally there is an observer in this system, who can stop the spin of a planet.

 

[RajeshTrivedi]

This problem just came to my mind. I am wondering, what could be its solution. Here it is:

Consider an isolated system. So there is no energy transfer from/to this system to/from outside.

There is an observer with n identical balls with him in this system. Consider n>2. Initially these balls are at rest with relative to the observer. Now the observer applies some force to these balls. All these balls are spinning. Consider the conservation of angular momentum. These balls will spin in such a fashion, that their angular momentum is conserved.

After some time, the observer holds one ball and stopped its spin. Will it change the spin of other (n-1) balls, so that their angular momentum is conserved?

1. Observer is the part of your system, how did he make the balls spin in the start? How did he stop one ball? In absence of gravity or any other leveraging force balls+observer angular momentum will be conzerved. This is classical. If you feel to invoke relativity here, then define the system and involvement of inter balls gravity first.

 

[hansda]

1. Observer is the part of your system,

YES. You can consider the observer as a Human Being who can interact with the balls. The observer can give energy to the balls. The observer also can stop the spin of the balls.

how did he make the balls spin in the start?

Initially all these balls were at rest with relative to the observer. Through some mechanism, he applied spin to these balls.

How did he stop one ball?

By holding it.

In absence of gravity or any other leveraging force balls+observer angular momentum will be conzerved. This is classical.

Why you are thinking, there is absence of gravity. Two mass will attract each other. This is classical/Newtonian concept of gravitational force.

If you feel to invoke relativity here, then define the system and involvement of inter balls gravity first.

Isn't angular momentum conserved in relativity?

 

[river]

Here's the thing about ; angular momentum conservation in relativity

http://physics.stackexchange.com/qu...what-is-it-is-it-conserved-and-how-do-we-know

Hansda; excellent question

 

[hansda]

Here's the thing about ; angular momentum conservation in relativity

http://physics.stackexchange.com/qu...what-is-it-is-it-conserved-and-how-do-we-know

Hansda; excellent question

Thanks for the link.

 

[river]

Thanks for the link.

Your welcome

But make no mistake , I will challenge you . as it should be , but with civility , as it should be .

river

 

[origin]

When the spinning ball is stopped by the observer, its kinetic energy may be converted into potential energy. How its angular momentum is conserved? Is it absorbed by the atomic particles or photons?

When the spinning ball is stopped by the observer the observer/ball will begin to spin at a much slower rate. If the observer is attached to the rest of the system (like standing on the floor) then the entire system will begin to rotate. The angular momentum is conserved through the entire mass that is rotating. The kinetic energy is not converted to potential energy.

It seems that your question has be satisfactorally answered but you continue to ask questions about this system. Is there some specific question that you feel has not been answered?

 

[river]

When the spinning ball is stopped by the observer the observer/ball will begin to spin at a much slower rate.

Don't follow your logic

The ball is stopped .

If the observer is attached to the rest of the system (like standing on the floor) then the entire system will begin to rotate. The angular momentum is conserved through the entire mass that is rotating. The kinetic energy is not converted to potential energy.

Not if the angular momentum is stopped

 

[river]

The angular momentum is lost .

The momentum , kinetic energy is aborbed through the observer .

The observer loses the kinetic energy or better , distributes the kinetic energy through out its self . dissipates this kinetic energy .

Much like a collision , the kinetic energy is absorbed and distributed throughout the object .

And therefore the kinetic energy is stopped .

 

[Sarkus]

If the system has net positive angular momentum then it will always have net positive angular momentum. If it has zero angular momentum then it will always have zero.
If it has positive net angular momentum then when you say "not if the angular momentum is stopped" can not be with regard the whole system - only with individual elements within the system but not to all the elements.

So imagine the scenario where the observer has zero angular momentum and the ball has X (with reference to a particular axis).
If the observer stops the angular momentum of the ball then the system (the ball and the observer) still have X, but if the ball's angular momentum is zero then the observer must now have X.

It is the same for any other property that is conserved: the system in question ALWAYS has the same amount of that property. If it doesn't always have the same amount then it is, by definition, not conserved.
Angular momentum is a conserved property.

 

[river]

If the system has net positive angular momentum then it will always have net positive angular momentum. If it has zero angular momentum then it will always have zero.
If it has positive net angular momentum then when you say "not if the angular momentum is stopped" can not be with regard the whole system - only with individual elements within the system but not to all the elements.

So imagine the scenario where the observer has zero angular momentum and the ball has X (with reference to a particular axis).
If the observer stops the angular momentum of the ball then the system (the ball and the observer) still have X, but if the ball's angular momentum is zero then the observer must now have X.

It is the same for any other property that is conserved: the system in question ALWAYS has the same amount of that property. If it doesn't always have the same amount then it is, by definition, not conserved.
Angular momentum is a conserved property.

Disagree

Read my last post # 14

 

[Sarkus]

Thats true. I only mentioned gravity, because through gravity a mass can interact with other mass; be it Newtonian gravity or GR.

Okay, but angular momentum is still conserved within a given closed system.

When the spinning ball is stopped by the observer, its kinetic energy may be converted into potential energy. How its angular momentum is conserved? Is it absorbed by the atomic particles or photons?

If the angular momentum is stopped by the observer, the observer takes on the angular momentum. This is basic conservation: the sum total of the conserved property does not change within a closed system. Angular momentum is a conserved property. If one element of the system changes angular momentum, the other(s) that interacted with it to cause it to change its angular momentum must then pick up the difference.

Not very correct. In Newtonian Gravity, this may be correct but in GR this may not be correct. In Newtonian Gravity spin does not play any role in gravity but in GR spin may cause additional curvature to spacetime causing Frame-Dragging effect. In Newtonian Gravity, there may be an effect of precession also, causing a little change in the angular momentums.

If the other balls are interacting then they are part of the system. I was referring to where the observer only interacts with the one ball. This is the simplest case (observer plus 1 ball).

Whatever the angular momentum, at the time of Big-Bang; Say it is conserved at every moment of time. So, it is the same angular momentum now.

Yes. Which is why it is quite possibly a net-zero sum, much like the energy of the universe is thought to be.

What kind of interaction, you are considering here?

It could be any sort of interaction. Anything that causes an effect on the other member of the system.

The smaller system(as defined by you as the interaction of observer with one of the balls) also can interact with larger system through gravity.

Yes - but I was rather specific in what I said: "But when the observer interacts with one of the balls, and neither is also acting in any way with anything else".

I think you are not considering the interaction through gravity or effect of precession or effect of Frame-Dragging here.

And you'd be wrong. Whatever the means of interaction, the property of angular momentum is conserved.

For a better visualization of this problem, consider an isolated solar system with n identical planets spinning around their centre of mass. Additionally there is an observer in this system, who can stop the spin of a planet.

Yet the angular momentum of the system remains the same. Whatever the interactions, if those interactions can impart angular momentum on the other members of the system, then a change in one will affect the others through those interactions such that the net angular momentum of the system does not change.
If an observer stops the spin of one ball then the angular momentum of the ball will classically be imparted to the observer+ball combination.
If other interactions exist between the ball, observer and other balls that might affect the angular momentum of those other elements, then the change in angular momentum in the one ball might affect the angular momentum of those other elements through the way they are interacting.
But these other interactions will be very small indeed in comparison to the transfer due to physical contact.

 

[Sarkus]

Disagree

Read my last post # 14

You can disagree all you want, river. But in this you'll continue to be wrong.
I sugget you brush up on your physics, and get a basic understanding of which properties in physics are conserved.

 

[river]

Okay, but angular momentum is still conserved within a given closed system.

How so ?

Angular momentum is kinetic . and kinetic energy can reach the point of zero .

 

[Sarkus]

How so ?

Angular momentum is kinetic . and kinetic energy can reach the point of zero .

Energy as a whole is conserved, not necessarily just kinetic energy. E.g. when you throw a ball up in a vacuum the ball gains potential energy as it loses kinetic energy until it reaches its highest (max potential energy while kinetic is zero) and then gains kinetic as it loses potential on its way down.

Angular momentum as a whole is conserved.