In the angular momentum equation, L = r x p, when the magnitude of the radius changes, which one of the remaining variables is correctly conserved ?

[Mandlbaur]

It does not exhibit rotation around a central point therefore your argument does not pertain to my paper.

[KipIngram]

Abstract:

Both angular momentum and momentum are accepted to be conserved values and both of these are contained within the equation L = r x p. Assuming the implied rotation around a central point, they cannot both be conserved when the magnitude of the radius changes. The generally accepted principle is that momentum must change in order to conserve angular momentum. However it is logically proven that it is the component of momentum perpendicular to the radius which must be conserved.

Introduction:

Whilst working on a project which did not achieve the results predicted by physics, I stumbled upon this.

Proof:

For the equation L = r x p¹. Assuming the implied rotation around a central point.

Premise 1:

There is a force at all times directed from the point mass along the radius toward the centre of rotation (centripetal force).

Premise 2:

A change in the magnitude of radius is conducted by altering the magnitude of this force.

Premise 3:

There can be no component of this force perpendicular to the radius.

Premise 4:

In order to affect the component of momentum perpendicular to the radius, we have to apply a parallel component of force (Newton’s first law).

Deduction:

A change in the magnitude of the radius cannot affect the component of momentum perpendicular to the radius.

Conclusion:

In the equation L = r x p, assuming the implied rotation around a central point, it is the component of momentum perpendicular to the radius which must be conserved when the magnitude of the radius changes.

References:

1) D.Halliday & R.Resnick, Fundamentals of Physics, second edition, extended version (John Wiley & Sons, Inc , New York, 1981) p. 181.

 

You did specify zero torque in your OP - premise 1 and premise 3. Each of those describes a central force. Therefore angular momentum is conserved.

 

Imagine that you lay a Cartesian x/y coordinate system down on top of your system, with the central point at the origin and such that at time t the radius vector lies along the x axis. You then stipulate that the force is directed along the x axis at that time. So the y component of momentum is conserved, but the x component is not.

 

Shortly later, the radius vector is no longer parallel with the x axis. Therefore the x component of momentum now contributes to the component of momentum perpendicular to the (new) radius vector.

 

So the force cannot affect the component of momentum perpendicular to the radius vector now, but it does affect the component of momentum that will be perpendicular to the radius vector later.

 

This is why the speed of the object can change.

 

These are really fundamental things, and we've explained them to you several ways - you're starting to come off as stubborn about this.

[swansont]

Abstract:

Both angular momentum and momentum are accepted to be conserved values and both of these are contained within the equation L = r x p. Assuming the implied rotation around a central point, they cannot both be conserved when the magnitude of the radius changes. The generally accepted principle is that momentum must change in order to conserve angular momentum. However it is logically proven that it is the component of momentum perpendicular to the radius which must be conserved.

 

 

(1) Linear momentum is conserved when there is no net external force.

(2) Angular momentum is conserved when there is no net external torque.

 

Under the presence of a force, which must be present for rotational motion, condition (1) is violated.

 

If the p component perpendicular to radius is conserved and L and p cannot both be conserved, how is it possible to conserve L?

 

That has already been answered. The change in p and r are inversely related.

[Mandlbaur]

 

 

(1) Linear momentum is conserved when there is no net external force.

(2) Angular momentum is conserved when there is no net external torque.

 

Under the presence of a force, which must be present for rotational motion, condition (1) is violated.

 

 

That has already been answered. The change in p and r are inversely related.

 

This is correct and very deep, but is it not a common known fact that a perpendicular force changes the direction but not the magnitude of the velocity?

[swansont]

If the p component perpendicular to the radius is conserved, then when the radius stops changing, the magnitude of p will be the same as it was initially. i.e.: p is conserved and L therefore cannot be.

 

You can't have this condition unless there is a net torque on the system.

 

In the angular momentum equation, angular momentum(L) = radius® x momentum(p), when the magnitude of the radius changes, which one of the remaining variables is correctly conserved ?

 

Without specifying whether or not you are applying a torque, you can't tell.

[Mandlbaur]

 

You can't have this condition.

 

 

Without specifying whether or not you are applying a torque, you can't tell.

 

We have covered this previously, since I do not mention a torque, I am not applying a torque.

[swansont]

 

This is correct and very deep, but is it not a common known fact that a perpendicular force changes the direction but not the magnitude of the velocity?

 

 

We went over this in another thread, If you ignore answers you don't like , this will be an issue. You need to describe how, exactly, the radius is changing, i.e the mechanism. You will find that there is a tangential force.

 

We have covered this previously, since I do not mention a torque, I am not applying a torque.

 

No, it means you are ignoring torque, and that's why your argument fails.

 

This is the flaw of a "logical" argument. It is very easy to make a statement that violates physical law, and thus gives rise to an apparent contradiction. It's how people argue for perpetual motion, or against relativity.

[Mandlbaur]

 

 

We went over this in another thread, If you ignore answers you don't like , this will be an issue. You need to describe how, exactly, the radius is changing, i.e the mechanism. You will find that there is a tangential force.

 

 

Since this paper is new and had not yet been presented when we had the previous discussion, the arguments in the previous thread do not match. I believe that I have described the mechanism whereby the radius changes. However since you would like a more in depth explanation: If the centripetal force is either larger or insufficiently large enough to maintain the radius at exactly the same magnitude, then the radius will change. Since the centripetal force is acting directly along the radius, am I incorrect in believing that there can be no tangential force?

[swansont]

Since this paper is new and had not yet been presented when we had the previous discussion, the arguments in the previous thread do not match.

The arguments may not match but the error is consistent.

 

I believe that I have described the mechanism whereby the radius changes. However since you would like a more in depth explanation: If the centripetal force is either larger or insufficiently large enough to maintain the radius at exactly the same magnitude, then the radius will change. Since the centripetal force is acting directly along the radius, am I incorrect in believing that there can be no tangential force?

If you carefully analyze the system, you will see what's going on. You could have an elliptical orbit, in which case there is no problem with the speed changes, or you actually have a tangential force. It will depend on the details of the system being analyzed, and I believe this has been pointed out to you before by studiot.

[KipIngram]

 

 

Since this paper is new and had not yet been presented when we had the previous discussion, the arguments in the previous thread do not match. I believe that I have described the mechanism whereby the radius changes. However since you would like a more in depth explanation: If the centripetal force is either larger or insufficiently large enough to maintain the radius at exactly the same magnitude, then the radius will change. Since the centripetal force is acting directly along the radius, am I incorrect in believing that there can be no tangential force?

 

That's not how I read your premises - that they implied no force perpendicular to the radius vector. And that is exactly when angular momentum is conserved.

 

But that isn't the same as no tangential force. There is no force perpendicular to the radius. In circular motion that is the same as "no tangential force." But in elliptical motion that is not true, because in elliptical motion the motion is not everywhere perpendicular to the radius (if it were the radius would never change). So there is a force component parallel to *motion* at some locations along an elliptical path.

 

Edit: Sorry - crossposted with swansont.

In other words, yes, you are incorrect in saying there is no tangential force.

Edited June 4, 2017 by KipIngram

[Mandlbaur]

 

You did specify zero torque in your OP - premise 1 and premise 3. Each of those describes a central force. Therefore angular momentum is conserved.

 

Imagine that you lay a Cartesian x/y coordinate system down on top of your system, with the central point at the origin and such that at time t the radius vector lies along the x axis. You then stipulate that the force is directed along the x axis at that time. So the y component of momentum is conserved, but the x component is not.

 

Shortly later, the radius vector is no longer parallel with the x axis. Therefore the x component of momentum now contributes to the component of momentum perpendicular to the (new) radius vector.

 

So the force cannot affect the component of momentum perpendicular to the radius vector now, but it does affect the component of momentum that will be perpendicular to the radius vector later.

 

This is why the speed of the object can change.

 

These are really fundamental things, and we've explained them to you several ways - you're starting to come off as stubborn about this.

 

 

With this scenario that you describe, would I be correct in saying that a positive centripetal force would result in a positive contribution to the perpendicular momentum of the "radius vector later"?

[studiot]

It does not exhibit rotation around a central point therefore your argument does not pertain to my paper.

 

So can I take it you are denying that a wheel rotates about its hub?

[Mandlbaur]

 

So can I take it you are denying that a wheel rotates about its hub?

 

 

Thank you for pointing out a flaw in my work, I should have referred to a fixed central point. I will put that into my revision.

[studiot]

 

 

Thank you for pointing out a flaw in my work, I should have referred to a fixed central point. I will put that into my revision.

 

+1

 

I was not I who chose this confrontational approach to the discussion.

 

I far prefer cooperation and pooling of knowledge.

 

You may like to know that both my questions were very very simple examples of the sort of calculations engineers do every day when considering the complicated dynamics of machinery and in fluid mechanics in general.

This would include deriving suitable equations to describe the motion of moving parts and the forces (and moments) they exert upon one another.

 

I come back to this point about conservation being a system property not an equation property.

 

The same problem bedevils another field entirely - that of Thermodynamics.

 

So many would be engineers fail simply because they do not properly identify the system.

Edited June 4, 2017 by studiot

[Mordred]

This is why looking over the mathematical proofs for conservation of energy is important. Part of the proof is defining a closed system. The other part shows the torque aspects. The proof also identifies which vectors are involved.

[imatfaal]

 

...

 

The same problem bedevils another field entirely - that of Thermodynamics.

 

So many would be engineers fail simply because they do not properly identify the system.

This. The first parts of the MIT advanced mechanics course were

 

1. Identify the System

2. Ensure you have identified the system correctly

[Mandlbaur]

 

+1

 

I was not I who chose this confrontational approach to the discussion.

 

I far prefer cooperation and pooling of knowledge.

 

You may like to know that both my questions were very very simple examples of the sort of calculations engineers do every day when considering the complicated dynamics of machinery and in fluid mechanics in general.

This would include deriving suitable equations to describe the motion of moving parts and the forces (and moments) they exert upon one another.

 

I come back to this point about conservation being a system property not an equation property.

 

The same problem bedevils another field entirely - that of Thermodynamics.

 

So many would be engineers fail simply because they do not properly identify the system.

 

 

This is why looking over the mathematical proofs for conservation of energy is important. Part of the proof is defining a closed system. The other part shows the torque aspects. The proof also identifies which vectors are involved.

 

 

The fact that I concede a mistake in my paper about referring to a fixed central point as opposed to a central point does not mean that I concede anything regarding the point that I am trying to get across.

 

I do not believe that I have been confrontational at all - that implication is a false.

 

My paper still stands, it still has not faced any argument which faults any of its premisses nor flaws any logic which is required in order to dismiss it.

 

I have faced every challenge posed and I believe that so far have defeated all of the important ones.

 

My aim is not confrontation, I am simply trying to get my point across.

[KipIngram]

?? If your premise is that angular momentum is not conserved in a central force system, then you are simply wrong and we've pointed that out to you in a variety of ways.

 

What is your ultimate goal here? Let's say you were right, and you can construct a case where angular momentum isn't conserved. Where do you go from there? Is the next step the description of some sort of "free energy device"?

[Mordred]

I'm not trying to be confrontational. I am trying to get you to fully examine the problem at hand. Not just handwave counter arguments.

 

Simply because you chose to not include torque does not make your logic argument correct. I quoted a particular line in your proof that would have provided insight as to why the conservation of angular momentum specifies torque in its very definition.

 

Looking at the mathematical proof would have identified the requirement on the quoted section.

 

(as already pointed out premise 1 and 3)

 

There is numerous mathematical proofs and methodologies my personal favourite being Noethers theorem under rotational invariance however there are other mathematical proofs.

 

Just a side note when trying to develop a new model or understanding its always best to provide the current understandings and mathematics then show the errors.

 

This also shows you have a decent knowledge and understanding of said topic.

Edited June 4, 2017 by Mordred

[studiot]

 

 

 

 

The fact that I concede a mistake in my paper about referring to a fixed central point as opposed to a central point does not mean that I concede anything regarding the point that I am trying to get across.

 

I do not believe that I have been confrontational at all - that implication is a false.

 

My paper still stands, it still has not faced any argument which faults any of its premisses nor flaws any logic which is required in order to dismiss it.

 

I have faced every challenge posed and I believe that so far have defeated all of the important ones.

 

My aim is not confrontation, I am simply trying to get my point across.

 

There is more than a mistake in your thinking, there is a fundamental misunderstanding.

 

Your stipulation concerning rotation about a 'fixed point' just won't wash.

 

Consider the following.

 

Somerset is famous for the largest nightime illuminated carnival in the world.

This is made from hundreds of floats which are made from enormous low loader lorries.

Mounted on these lorries are carousels, roundabouts and other rotating mechanisms, carrying carnival actors.

 

Now tell me that your analysis debars these actors from claiming that these carousels rotate about a fixed point whilst spectators on the sidewalks claim the point is moving along on the back of a lorry.

 

There is a considerable amount you clearly don't know so rudely telling a bunch of folks with Phds in engineering and/or physics that they don't know what they are talking about and only you are correct is in my view confrontational.

 

The sad thing is that your formula can be applied (if done correctly) to these carousels or my wheel, but your are refusing to allow that anyone else knows anything.

 

In more advanced mechanics this issue is resolved by means of one of two methods that of Lagrange or that of Euler, one of which takes the view of the spectator the other the view of the carousel actor.

 

Have you heard of these?

[Mandlbaur]

I'm not trying to be confrontational. I am trying to get you to fully examine the problem at hand. Not just handwave counter arguments.

 

Simply because you chose to not include torque does not make your logic argument correct. I quoted a particular line in your proof that would have provided insight as to why the conservation of angular momentum specifies torque in its very definition.

 

Looking at the mathematical proof would have identified the requirement on the quoted section.

 

(as already pointed out premise 1 and 3)

 

There is numerous mathematical proofs and methodologies my personal favourite being Noethers theorem under rotational invariance however there are other mathematical proofs.

 

Just a side note when trying to develop a new model or understanding its always best to provide the current understandings and mathematics then show the errors.

 

This also shows you have a decent knowledge and understanding of said topic.

 

 

I have already asked you whether it is necessary for me to prove every other derivation wrong before you will consider my work. This was a non-confrontational way of trying to point out to you that it is not necessary.

 

Seriously, others have even pointed out that your torque argument does not hold water. How does a person tackle an argument that someone refuses to give up on even when it has been defeated on multiple occasions other than by confrontation?

 

I have a knowledge of the topic because of my work which included the design, manufacture and testing of many experimental prototypes. Each one an optimised version of the previous model. All of them attempts to achieve extremely high magnitudes of angular velocity predicted by conservation of angular momentum. All of them indicating that angular momentum is not conserved in variable radii systems.

 

I have spent much time trying to understand why and have discovered the truth and pinpointed the problem. I have written three different proofs of this. This paper being the latest iteration of my second proof.

 

Clearly this is extremely difficult for people to accept. I understand that it is akin to physical pain for a person to have to change their world view. I'm sorry about that.

 

Unfortunately because I am the one who has stumbled on this, I am tasked with getting it known and therefore have no option but to continue to push this heavy stone up this endless hill until somebody listens.

[KipIngram]

studiot makes a good point - in fact both of the particles in your model will move. The system will have a fixed center of mass, and both particles will move around it. Your "fixed central point" scenario is the limit as the central mass becomes >> than the other mass, but it never applies fully.

No - if your experiments seem to be showing that angular momentum isn't conserved then you are overlooking a source of external torque.

[Mordred]

Why do you think you need to disprove every single derivitative involved?

 

Have you studied the mathematical proof for conservation of angular momentum? There isn't that many formulas involved in the proof.

 

Simple denial doesn't cut it

 

Demonstrate to us a proper understanding of how conservation of angular momentum works. A logic argument isn't sufficient considering it is literally someone elses work.

 

Demonstrate you properly understand the premises involved. ie premise 1 and 3

 

Thus far all your demonstrating is a lack of understanding behind the premises you posted. (prove to me otherwise please)

I am specifically asking you to demonstrate a working knowledge of why this is the case...

 

Under Noethers theorem if you assign the referred to axis as N then the action L is conserved along the N axis.

 

see rotational invariance

 

https://en.m.wikipedia.org/wiki/Noether%27s_theorem

 

In particular

 

"In other words, the component of the angular momentum L along the n axis is conserved."

I went and hit the wrong button and editted a previous post.

 

I meant this to be here lol

 

Anyways this demonstrates the premise 1 and 3

Edited June 4, 2017 by Mordred

[Mandlbaur]

studiot makes a good point - in fact both of the particles in your model will move. The system will have a fixed center of mass, and both particles will move around it. Your "fixed central point" scenario is the limit as the central mass becomes >> than the other mass, but it never applies fully.

No - if your experiments seem to be showing that angular momentum isn't conserved then you are overlooking a source of external torque.

 

 

?? If your premise is that angular momentum is not conserved in a central force system, then you are simply wrong and we've pointed that out to you in a variety of ways.

 

What is your ultimate goal here? Let's say you were right, and you can construct a case where angular momentum isn't conserved. Where do you go from there? Is the next step the description of some sort of "free energy device"?

 

Answer my previous question to you. This will indicate once again that your "pointing out" is been flawed. There is nothing you have "pointed out" that I have not defeated.

 

Unfortunately I can't defeat a confirmation bias.

 

 

 

There is more than a mistake in your thinking, there is a fundamental misunderstanding.

 

Your stipulation concerning rotation about a 'fixed point' just won't wash.

 

Consider the following.

 

Somerset is famous for the largest nightime illuminated carnival in the world.

This is made from hundreds of floats which are made from enormous low loader lorries.

Mounted on these lorries are carousels, roundabouts and other rotating mechanisms, carrying carnival actors.

 

Now tell me that your analysis debars these actors from claiming that these carousels rotate about a fixed point whilst spectators on the sidewalks claim the point is moving along on the back of a lorry.

 

There is a considerable amount you clearly don't know so rudely telling a bunch of folks with Phds in engineering and/or physics that they don't know what they are talking about and only you are correct is in my view confrontational.

 

The sad thing is that your formula can be applied (if done correctly) to these carousels or my wheel, but your are refusing to allow that anyone else knows anything.

 

In more advanced mechanics this issue is resolved by means of one of two methods that of Lagrange or that of Euler, one of which takes the view of the spectator the other the view of the carousel actor.

 

Have you heard of these?

 

 

Any system to which the formula I have specified in my paper can be realistically applied is proven by my paper to not conserve angular momentum when the radius changes.

 

I am not trying to prove to anybody how clever I am.

 

I am completely dumb in your shadow.

 

Sometimes a dumb person does have a point.

 

This is one of those occasions.

Why do you think you need to disprove every single derivitative involved?

 

Have you studied the mathematical proof for conservation of angular momentum? There isn't that many formulas involved in the proof.

 

Simple denial doesn't cut it

 

Demonstrate to us a proper understanding of how conservation of angular momentum works. A logic argument isn't sufficient considering it is literally someone elses work.

 

Demonstrate you properly understand the premises involved. ie premise 1 and 3

 

Thus far all your demonstrating is a lack of understanding behind the premises you posted. (prove to me otherwise please)

I went and hit the wrong button and editted a previous post.

 

I meant this to be here lol

 

Anyways this demonstrates the premise 1 and 3

 

My point is actually that I should not be required to have to prove or disprove anything about any other theory prior to my work being considered.

 

I don't understand the rest of your post. Are you seriously claiming that I don't understand my own premisses? Surely I would not have been able to create them if I didn't understand them?

[KipIngram]

My point is actually that I should not be required to have to prove or disprove anything about any other theory prior to my work being considered.

 

Well, in point of fact you do - you have to get others to choose to take you seriously in order to get your work considered. I think today hasn't been a very good day for you in that respect.

 

One last time: angular momentum is conserved in all closed systems. If you have accurately measured some apparatus exhibiting a changing angular momentum, then it is not a closed system. End of story, and I am done here.