A simple classical physics / algebra question

[Mandlbaur]

If we define a variable a = b * c. Where b and c are independent, unrelated variables and b is not zero. Can we then say with confidence that if we change c, a will change ?

If so, then why is it not acceptable to say that since angular momentum is defined as radius cross product momentum and momentum and radius are independent, unrelated variables that as long as the momentum is not zero, if we change the magnitude of the radius, the magnitude of the angular momentum will change ?

[timo]

The answer to your first question is: Not necessarily. If a, b, and c are real numbers and * is the multiplication of the reals then the statement is true. In case of vectors and the cross product a counter-example would be b = (1, 0, 0) and c = (0, 1, 0) where b is changed to equal (1,1,0).

 

Since I assume that by "the momentum is not zero" you refer to the linear momentum then again the answer to your second question is "not necessarily". Take a radial vector (1,0,0) and a linear momentum (1,0,0). Changing the radial vector to (2,0,0) still leaves the angular momentum at zero. Your statement would work if the angular momentum was not zero, since scaling up the radial vector by a factor (while leaving the linear momentum constant) also scales up the resulting angular momentum by the same factor.

Edited March 6, 2017 by timo

[Mandlbaur]

I apologise.

 

If we include the proviso that the numbers are real numbers and that the angular momentum is not zero, then you agree that we can make both claims.

 

How is it possible then for angular momentum to be conserved when we change the radius ?

[Country Boy]

The answer to your original question, "if a= bc and we change c, will a change" is "not necessarily", for two reasons:

1) If b= 0, bc= 0 no matter what c is.

2) It is possible that b might change also so that bc stay equal to a.

 

Now you are asking "is it possible to conserve angular momentum if we change the radius. Again the answer is "yes, it I possible" again for two reasons:

1) if there is no motion, the angular momentum is 0 no matter what the radius is.

2) If we increase or decrease the radius, we could also decrease or increase the angular velocity so that the angular momentum stays the same.

Edited March 7, 2017 by Country Boy

[swansont]

I apologise.

 

If we include the proviso that the numbers are real numbers and that the angular momentum is not zero, then you agree that we can make both claims.

 

How is it possible then for angular momentum to be conserved when we change the radius ?

 

 

You are not constraining b (from your example) to remain fixed. If there is no net torque, however, you are constraining the angular momentum to be fixed. The angular speed must change if the radius is changed.

[Mandlbaur]

 

 

You are not constraining b (from your example) to remain fixed. If there is no net torque, however, you are constraining the angular momentum to be fixed. The angular speed must change if the radius is changed.

 

Timo is a scientist and a senior member and he has agreed that my first statement is true once we add the real number proviso without having to specify a constraint on b. I believe him.

He has also stated that the angular momentum will scale with the radial vector which implies that it is not constrained.

I agree with you that the angular speed will change because angular velocity is equal to velocity divided by radius.

Edited March 8, 2017 by Mandlbaur

[swansont]

 

Timo is a scientist and a senior member and he has agreed that my first statement is true once we add the real number proviso without having to specify a constraint on b. I believe him.

He has also stated that the angular momentum will scale with the radial vector which implies that it is not constrained.

I agree with you that the angular speed will change because angular velocity is equal to velocity divided by radius.

 

 

In the OP you say that "b and c are independent, unrelated variables". You also have the implication that, because you are changing c and b is independent, that b is not affected, i.e. it doesn't change. That is not the case when you apply this to angular momentum; the variables are no longer independent/unrelated.

[Mandlbaur]

 

 

In the OP you say that "b and c are independent, unrelated variables". You also have the implication that, because you are changing c and b is independent, that b is not affected, i.e. it doesn't change. That is not the case when you apply this to angular momentum; the variables are no longer independent/unrelated.

 

 

Prior to the definition of angular momentum, surely you would agree that radius and momentum could not reasonably have been described as related or interdependent.

 

Does the act of defining angular momentum as the cross product of these variables change their status?

[imatfaal]

 

 

Prior to the definition of angular momentum, surely you would agree that radius and momentum could not reasonably have been described as related or interdependent.

 

Does the act of defining angular momentum as the cross product of these variables change their status?

 

No - nature is just that way. It was the case before we or our planet came into existence and it will still be the case be once we have gone. Just because characteristics and qualities of objects have independent methods of measurement, and we see them as distinct does not mean that they are independent.

 

Is mass connected to velocity? - yes; because momentum is conserved in the absence of an external force. Must we always be concerned about an object's velocity in order to obtain its mass (or vice versa)? - no; because in many circumstances we either don't care about momentum or we are exerting an external force.

[Mandlbaur]

 

No - nature is just that way. It was the case before we or our planet came into existence and it will still be the case be once we have gone. Just because characteristics and qualities of objects have independent methods of measurement, and we see them as distinct does not mean that they are independent.

 

Is mass connected to velocity? - yes; because momentum is conserved in the absence of an external force. Must we always be concerned about an object's velocity in order to obtain its mass (or vice versa)? - no; because in many circumstances we either don't care about momentum or we are exerting an external force.

 

 

What evidence do we have that nature is that way?

[Bender]

Lots. Conservation of momentum has never been observed to be violated.

[Mandlbaur]

Lots. Conservation of momentum has never been observed to be violated.

 

 

I strongly disagree with that. Take the example of a professor performing the ball on a string demonstration. If his initial angular velocity is two revolutions per second and he reduces the radius to one tenth, which is very close to what is often performed. Currently accepted physics says that the angular velocity must increase 100 fold. 200 revolutions per second is 12000 rpm. We have never observed anything close to this. We have observed plenty of violations - we have merely failed to recognise them as such.

[Strange]

 

 

I strongly disagree with that. Take the example of a professor performing the ball on a string demonstration. If his initial angular velocity is two revolutions per second and he reduces the radius to one tenth, which is very close to what is often performed. Currently accepted physics says that the angular velocity must increase 100 fold. 200 revolutions per second is 12000 rpm. We have never observed anything close to this. We have observed plenty of violations - we have merely failed to recognise them as such.

 

 

A vague description of a hypothetical experiment with no measurements being made does not invalidate a well established theory.

 

If you were to do some actual measurements and demonstrate that momentum is not conserved then you could be on your way to a Nobel Prize.

[Mandlbaur]

 

 

A vague description of a hypothetical experiment with no measurements being made does not invalidate a well established theory.

 

If you were to do some actual measurements and demonstrate that momentum is not conserved then you could be on your way to a Nobel Prize.

 

 

We can observe this experiment or very similar performed many times by many different people including many professors on youtube and in lecture halls so it can hardly be described as hypothetical. These professors have as yet failed to take measurements which means that the theory has been established due to an oversight. Since the predicted result is so absurdly high and obviously inaccurate, measurements are superfluous. A reasonable person must surely conclude purely from observation that 12000rpm is incorrect by an order of magnitude.

[Strange]

 

 

We can observe this experiment or very similar performed many times by many different people including many professors on youtube and in lecture halls so it can hardly be described as hypothetical. These professors have as yet failed to take measurements which means that the theory has been established due to an oversight. Since the predicted result is so absurdly high and obviously inaccurate, measurements are superfluous. A reasonable person must surely conclude purely from observation that 12000rpm is incorrect by an order of magnitude.

 

 

So you are suggesting we discard thousands of highly accurate experiments based on your impressions of something you saw on yootoob?

 

That is not how science works.

[Mandlbaur]

No, this is just an example provided to support my original logical argument and to refute the inaccurate claim that there has never been a violation observed.

[Argent]

No, this is just an example provided to support my original logical argument and to refute the inaccurate claim that there has never been a violation observed.

Any time I have seen, or performed, the ball-on-a-string experiment the centre point of rotation does not remain fixed. but moves. Unless you can show that movement does not occur, or provide the mathematics to demonstrate that alone cannot account for what you assert is an anomaly, you claim can be dismissed.

[Mandlbaur]

Any time I have seen, or performed, the ball-on-a-string experiment the centre point of rotation does not remain fixed. but moves. Unless you can show that movement does not occur, or provide the mathematics to demonstrate that alone cannot account for what you assert is an anomaly, you claim can be dismissed.

 

Since this experiment is the classical experiment used for centuries to convince students of the existence of conservation of angular momentum, it cannot be easily dismissed. Your claim that this demonstration of conservation of angular momentum is flawed merely supports my assertion that we have been misled which is exactly the point I am making with this example. We are not talking about a small difference here, we are talking about an order of magnitude so it can hardly be described as an "anomaly". In any event, I reiterate that this is purely an example provided to support my argument and it is not the basis of my argument and therefore my claim cannot be dismissed.

[Strange]

It is not an experiment, as it is completely unquantified.

 

Like many such classroom demonstrations it is pretty much bogus. For example, the teacher has to continually provide input to keep the ball spinning. As such, they control the speed of the spin. They could, if they chose, make it spin faster when long.

 

So it also a good demonstration of the teaching technique called "lies to children".

[Argent]

 

Since this experiment is the classical experiment used for centuries to convince students of the existence of conservation of angular momentum, it cannot be easily dismissed. Your claim that this demonstration of conservation of angular momentum is flawed merely supports my assertion that we have been misled which is exactly the point I am making with this example. We are not talking about a small difference here, we are talking about an order of magnitude so it can hardly be described as an "anomaly". In any event, I reiterate that this is purely an example provided to support my argument and it is not the basis of my argument and therefore my claim cannot be dismissed.

There seem to be some assumptions in your post. I am always nervous when an argument, or its defense is laden with assumptions.

 

I think you are mistaken in believing that the intent of the experiment is to "convince students of the existence of angular momentum". No proper science education would use an uncontrolled "experiment" of this sort to convince anyone. It is a useful demonstration of the principle, nothing more. Conviction must arise from a properly constructed experiment with appropriate measurements made to a requisite degree of accuracy.

 

I have not claimed that the demonstration is flawed. (Actually, that is not an assumption on your part, but a misreading of what I have written. Sorry I wasn't clearer.) I have claimed that is a demonstration. Again, you have taken a convenient classroom demonstration and assumed it is something more than that.

 

One is only misled if one assumes that a simplified demonstration meets the same criteria as a rigorously conducted, accurately measured physics experiment. I am guessing (not assuming) that you don't have much experience with teaching. Simplification and generalities are important aspects of teaching at the basic level.

 

OK, another point that is not really an assumption. If the magnitude of any difference between predicted and actual values exceeds what theory would expect then, regardless of that magnitude, it is correct to call it anomaly.

 

As an example it does not support your argument. You have yet to provide any evidence that supports your argument. Until you do there is no sound reason to entertain it beyond conducting this dialogue for a short time more.

 

Edited Comment: I have cross posted with Strange. He has said about the same as I did with fewer words. You might want to reconsider.

Edited March 12, 2017 by Argent

[swansont]

We can observe this experiment or very similar performed many times by many different people including many professors on youtube and in lecture halls so it can hardly be described as hypothetical.

 

 

Then you should have no trouble presenting some links to these observations.

[Mandlbaur]

There seem to be some assumptions in your post. I am always nervous when an argument, or its defense is laden with assumptions.

 

I think you are mistaken in believing that the intent of the experiment is to "convince students of the existence of angular momentum". No proper science education would use an uncontrolled "experiment" of this sort to convince anyone. It is a useful demonstration of the principle, nothing more. Conviction must arise from a properly constructed experiment with appropriate measurements made to a requisite degree of accuracy.

 

I have not claimed that the demonstration is flawed. (Actually, that is not an assumption on your part, but a misreading of what I have written. Sorry I wasn't clearer.) I have claimed that is a demonstration. Again, you have taken a convenient classroom demonstration and assumed it is something more than that.

 

One is only misled if one assumes that a simplified demonstration meets the same criteria as a rigorously conducted, accurately measured physics experiment. I am guessing (not assuming) that you don't have much experience with teaching. Simplification and generalities are important aspects of teaching at the basic level.

 

OK, another point that is not really an assumption. If the magnitude of any difference between predicted and actual values exceeds what theory would expect then, regardless of that magnitude, it is correct to call it anomaly.

 

As an example it does not support your argument. You have yet to provide any evidence that supports your argument. Until you do there is no sound reason to entertain it beyond conducting this dialogue for a short time more.

 

Edited Comment: I have cross posted with Strange. He has said about the same as I did with fewer words. You might want to reconsider.

 

 

Please provide a link to any properly conducted, controlled experiment used during the teaching of conservation of angular momentum showing a radius reduction which results in the claimed increase in magnitude of momentum?

Edited March 12, 2017 by Mandlbaur

[swansont]

Please provide a link to any properly conducted, controlled experiment used during the teaching of conservation of angular momentum showing a radius reduction which results in the claimed increase in magnitude of momentum?

Don't pass the buck. You claimed there were lots of videos where it obviously fails. Where are they?

[Bender]

Please provide a link to any properly conducted, controlled experiment used during the teaching of conservation of angular momentum showing a radius reduction which results in the claimed increase in magnitude of momentum?

Angular momentum can be mathematically derived from linear momentum. Are you aware of that fact, and as a result, do you also claim that linear momentum is not conserved and Newton's laws of motion are false?

[Mandlbaur]

Don't pass the buck. You claimed there were lots of videos where it obviously fails. Where are they?

 

 

Do you deny that this is and has been a common demonstration performed by professors for about three hundred years?

 

Do you assert that we might actually achieve 12000rpm when performing this demonstration?

 

The point of my last post was not to pass the buck, but to point out that there is no properly conducted controlled experiment supplied when teaching conservation of angular momentum. There is only the demonstrations. So science education does use an uncontrolled "experiment" in order to convince. Therefore in Argent's words: The science education is not proper.