# Angular momentum

Hi! Please, could someone tell me who defined angular momentum as r x P? Thank you.

Peter57

Sorry, not me. This is a weird question. What is it that you actually want to know ?

Meir Achuz
Homework Helper
Gold Member
Hi! Please, could someone tell me who defined angular momentum as r x P? Thank you.

Peter57
Newton used it and no one came before Newton.

Sorry, not me. This is a weird question. What is it that you actually want to know ?
I want to know who defined angular momentum as r x p. That is all,

Newton used it and no one came before Newton.
Thank you. Could you please give me some reference? It doesn't seem it was Newton who used it first.

It looks like my knowledge of the history of physics turned out to be somewhat useful after all. Before Newton and Galileo, the most commonly believed theory of physics was that of Aristotle and his followers. According to Aristotelian physics, the rest is the natural state and it requires a momentum in order to move an object. The concept of angular momentum came from this context, and the Aristotelian theory stated that it required a constant effort to keep an object in uniform circular motion.

It looks like my knowledge of the history of physics turned out to be somewhat useful after all. Before Newton and Galileo, the most commonly believed theory of physics was that of Aristotle and his followers. According to Aristotelian physics, the rest is the natural state and it requires a momentum in order to move an object. The concept of angular momentum came from this context, and the Aristotelian theory stated that it required a constant effort to keep an object in uniform circular motion.
Thank you very much. But would you know if Aristotle himself defined angular momentum as r x p? If he did not do it, somebody else must have done it. I would like to know who did it and why. I have reason to believe this definition is incorrect.

Wait, why do you think this definition is incorrect? It works remarkably well and leads to all manner of useful and accurate predictions.

D H
Staff Emeritus
The originator of $\vec l = \vec r \times \vec p$? It certainly was not Aristotle, Galileo, or Newton. The modern concept of vectors (and the cross product) was not "invented" until the mid 1800s.

Wait, why do you think this definition is incorrect? It works remarkably well and leads to all manner of useful and accurate predictions.
I found an experiment where r x p is not conserved when, clearly, no external torque acts on the object.

The originator of $\vec l = \vec r \times \vec p$? It certainly was not Aristotle, Galileo, or Newton. The modern concept of vectors (and the cross product) was not "invented" until the mid 1800s.
I think you are right. It is funny, although I have been asking far and wide, it seems nobody knows who was the first to use r x p.

D H
Staff Emeritus
The math before vector calculus was a bit convoluted. The concepts we use today existed nonetheless. In particular conservation of angular momentum is quite valid and predates this modern notation. Please explain your experiment.

Remember that "Extraordinary claims require extraordinary proof".

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I found an experiment where r x p is not conserved when, clearly, no external torque acts on the object.
Could you please describe the experiment to us so that we can help you clear any confusions?

russ_watters
Mentor
Perhaps if you explained the problem/experiment you are working on, we can help you understand the issue. Who originated this concept doesn't have anything to do with whether or no it is valid...

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that is what i used to think, and it would explain why angular velocity increases when the radius is smaller but it seems it is proportional to r^2 (mrv) so velocity increases too (angular velocity increases with 1/mr^2, being r^2 the moment of inertia). this is why it needs energy. if you have Serway's book (physics for scientists and engeneers) check out example 11.8 page 347).
I know physics textbooks teach angular momentum is mr^2w, but that is incorrect. For a point mass it is mrw. I wrote a paper on this subject, and a physics journal is now considering its publication.

Second try: Newton's second law is not violated. You have to apply a force to pull the object in, and that force accelerates the object. That's why it has a greater velocity (not just angular velocity) after you pull it in.

But I think Daniel already knows that. The question is why do you have to increase the tangential velocity when you pull it in, that is, what's up with this whole "angular momentum" conservation thing? Let's see if I can help now.

When the object is spinning around a circle, it constantly "wants" to keep going in a straight line, and the force that holds it on a circular path keeps pulling it in, always constantly bending its trajectory into a circle. The tighter the circle, the more its preferred straight path has to be bent, so the harder we have to pull to keep it going in a circle.

For this reason, if you want to make a tighter circle you have to pull harder. When you pull it in, you are doing work (applying a force over a distance), so you must be speeding the object up, increasing its linear momentum as well as angular momentum.

According to Newton's second law F(net) = dp/dt, only a net force in the direction of motion of an object, can change the magnitude of its velocity. A force perpendicular to the direction of motion of an object, does not change the magnitude of its velocity. If this were not true, a rotating object at the end of a string would increase its speed constantly, because it is subject to a constant centripetal force.

Hootenanny
Staff Emeritus
Gold Member
I know physics textbooks teach angular momentum is mr^2w, but that is incorrect. For a point mass it is mrw. I wrote a paper on this subject, and a physics journal is now considering its publication.
I'm afraid I disagree with you there. I also must warn you that according to the PF guidelines the discussion of theories which contradict mainstream beliefs is prohibited.
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I know physics textbooks teach angular momentum is mr^2w, but that is incorrect. For a point mass it is mrw. I wrote a paper on this subject, and a physics journal is now considering its publication.
Don't forget to let us know the name of the journal that has published this.

I'm afraid I disagree with you there. I also must warn you that according to the PF guidelines the discussion of theories which contradict mainstream beliefs is prohibited.
I am sorry to upset you, but I found an experiment that shows the currently accepted definition of angular momentum r x p is incorrect. That is why I was interested in knowing who defined angular momentum as r x p and why. Unfortunately, I have been unable to do it, so far at least. Anyway, I understand that, in physics, the experimental truth has the last word, and that should not be suppressed.

Hootenanny
Staff Emeritus
Gold Member
I am sorry to upset you, but I found an experiment that shows the currently accepted definition of angular momentum r x p is incorrect.
You haven't upset me in the slightest, I was simply making you aware that such discussions in this forum are prohibited.
Anyway, I understand that, in physics, the experimental truth has the last word, and that should not be suppressed.
I tend to agree with you there. As such PF has an https://www.physicsforums.com/forumdisplay.php?f=146".

However, I reiterate that the discussion of theories which contradict mainstream beliefs is prohibited in the main forums.

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The math before vector calculus was a bit convoluted. The concepts we use today existed nonetheless. In particular conservation of angular momentum is quite valid and predates this modern notation. Please explain your experiment.

Remember that "Extraordinary claims require extraordinary proof".
I am not questioning conservation of angular momentum at all, as I am not questioning the conservation of linear momentum. According to Webster's dictionary, momentum is: a property of a moving body that the body has by virtue of its mass and motion and that is equal to the product of the body's mass and velocity.

The way I understand it, angular momentum should be the momentum of an object in circular motion. In other words, linear and angular momentum are not two different kinds of momentum; they are the same thing. But linear and angular momentum, as currently understood, are two different kinds of momentum, with different units and different conservation laws; moreover, while linear momentum is a true vector, angular momentum is not, it is pseudovector, i.e., not a vector.

At this time, I cannot describe the experiment, because an application for a patent is in process, but I will as soon as I can.

Perhaps if you explained the problem/experiment you are working on, we can help you understand the issue. Who originated this concept doesn't have anything to do with whether or no it is valid...
Thank you. I will describe the experiment as soon as I can. In the meantime, do you agree that, according to Newton's second law F(net) = dp/dt, only a net force in the direction of motion of an object can change the magnitude of its velocity? In other words, a radial force on an object, like a satellite in a circular orbit, cannot change the magnitude of its velocity. I think this must be true; otherwise, the speed of a satellite in a circular orbit would increase constantly.

russ_watters
Mentor
I know physics textbooks teach angular momentum is mr^2w, but that is incorrect. For a point mass it is mrw. I wrote a paper on this subject, and a physics journal is now considering its publication.
We will be more than happy to consider your paper for discussion in our independent research forum, but until then we must insist that you not discuss it in the general physics sections of PF. We don't want to confuse people who come here to learn about what physics is today.

Don't forget to let us know the name of the journal that has published this.
I will as soon as it is published, if it is published.

We will be more than happy to consider your paper for discussion in our independent research forum, but until then we must insist that you not discuss it in the general physics sections of PF. We don't want to confuse people who come here to learn about what physics is today.
O. K. I agree.