Is the formula of the angular momentum conservation wrong?

[rlortie]

A little 'off topic' here. but the mention of strain on string reminds me of an episode happening many years ago!

A paper clip was hung on a string and suspended over a magnet. As the clip was lowered it begin spinning. This phenomena got a lot of excitement from members in various forums.

That is until it was explained that the magnet pull (strain) on the paper clip was causing the twisted thread strands to unwind! Oops! sorry no free rotation found here.

Ralph

[Dunesbury]

In the puck experiment, the pin simply changes the direction of movement. You are not forcing the puck into a smaller orbit against it's CF which would result in greater velocity and energy. Angular momentum is only conserved for a specific set of movements. The moving puck experiment is not unlike an object coasting along a curved path (no friction). It changes directions along the way, but it's velocity remains the same.

Angular momentum is always conserved, even in pin interrupted puck. Haven't we already covered this somewhere?

Pin doesn't add energy to system, so puck won't accelerate after new radius. In battery experiment, energy is added. It is simple as that.

[Furcurequs]

A little 'off topic' here. but the mention of strain on string reminds me of an episode happening many years ago!

A paper clip was hung on a string and suspended over a magnet. As the clip was lowered it begin spinning. This phenomena got a lot of excitement from members in various forums.

That is until it was explained that the magnet pull (strain) on the paper clip was causing the twisted thread strands to unwind! Oops! sorry no free rotation found here.

Ralph

Ralph,

...lol

When I began reading your post, only your first two paragraphs were on my screen. Before I even finished reading your second paragraph, I suspected the likely cause for the phenomenon was what I then scrolled down to read in your third paragraph.

Do you think the experimenters were too slow or just too optimistic?

I guess we all need to be careful about deceiving ourselves.

Dwayne

[zoelra]

Dunesbury,

There are a few examples of rotation where angular momentum is not conserved. One example is when a weight on a string wraps around a pole. Although there is inward movement, the weight continues to move around the pole at a constant translational velocity since there are no external forces that act to increase its velocity. Since v=rw, r and w are inversely proportional. r^2 and w have to be inversely proportional if angular momentum is to be conserved.

I believe that in the puck experiment, the pin simply changes the direction of movement causing no increase in velocity, just as the infinite number of points along the outside of the pole change the direction of the weight wrapping around it.

Attached is a thought experiment I had. It shows two weights (red and black) rotating CCW around their pivot points at the same translational velocity (v). Although the red weight completes two loops for each loop the black weight completes, they are timed so that when the black weight arrives at the 3 o'clock position, so does the red weight. In the picture I show the black weight slightly lower than the red so you can see both weights. At the instant the black string comes in contact with the red weights pivot point (the pin), the pin becomes the new pivot point for the black weight. At this time, both weights are at the 3 o’clock position, they are both moving at the same translational velocity (both in magnitude and direction), they have the same pivot point, and they are the same distance from the pivot point. My assumption is that both weights will continue moving around the shared pivot point at the same velocity (v). This analysis could be completely wrong so please let me know what you think.

[Fletcher]

Hi zoelra ..

Regarding your thought experiment - I think you would be correct - IINM both should circle the red pin/pivot together at the same speed.

In reality the black weight doesn't just transfer its connection to the red pin/pivot - it loops around it [because the pin/pivot has a small diameter] - this means the black weight will spiral inwards & increase its speed as its effecive radius decreases i.e. the string winds around the pin again & again - so the black weight will pull ahead [comparing to a radial line] of the red weight circling its pivot [co-located] & its linear velociy will increase to above the red weights due to CoAM, IINM.

[Furcurequs]

zoelra,

Please forgive me for this, but I need to restate what you are trying to say there with hopefully the correct terminology and even elaborate on some things. Some may want to believe I'm nitpicking, but since we only have so much to work with, I believe it's very important we try to get the fundamentals right, and some of the technical terms have very specific meanings.

Many here speak of "velocity" which, of course, is a vector quantity that has both magnitude and direction where they really mean to say "speed" which is a scalar quantity and would be the absolute magnitude of the velocity. Forces can, of course, change the velocity of a mass without necessarily changing its speed.

So, to quote you:

"Although there is inward movement, the weight continues to move around the pole at a constant translational velocity since there are no external forces that act to increase its velocity."

...and how I would say it:

Although there is inward movement, the weight continues to move at a constant SPEED along its spiraling path around the pole since the force supplied by the string accelerates the weight in such a way to change its translational velocity in direction alone.

So, the translational velocity is continuously changing as the weight spirals inward at a constant speed. The angular momentum of the weight around the center of the pole is continuously decreasing in its magnitude due to an exchange of angular momentum with the pole and the earth thanks to forces of acceleration transmitted through the string that aren't actually directed through the center of the pole itself. There are no forces, however, that increase the speed and thus the kinetic energy of the spiraling weight.

...erm, well, that is if we assume there is no change in the height of the spiraling weight in the gravitational field and thus no increase in kinetic energy due to a change in gravitational potential energy, of course, and we also ignore air drag and energy losses due to friction and whatnot. ...lol

Although the angular momentum of the weight itself around the center of the pole changes, the angular momentum of the earth, pole, string and weight system should be conserved when considered as a whole. That means there should also be a change in the angular momentum of the earth and pole themselves and thus a change in rotation of the earth and pole around the approximate center of the pole, but these changes are immeasurably small due to the relatively huge mass of the earth.

(I was also going to say that the angular velocity of the weight around the center of the pole would continuously increase, too, but upon reflection I'm not so sure if that's always the case - but may rather depend upon the pole diameter and the distance of the weight from the center of the pole at any given time. ...hmmm...)

Anyway...

As far as your thought experiment, change "translational velocity" and "velocity" to "speed" and I think you've essentially got it.

That's for a pin of negligible diameter and maybe only a few turns, of course. Otherwise, what Fletcher said about it. Well, still change "translational velocity" and "velocity" to "speed," though.


Dwayne

[Furcurequs]

Oops, after rereading Fletcher's post, maybe not what he said about it after all - until we clarify some things.

Hi zoelra ..

Regarding your thought experiment - I think you would be correct - IINM both should circle the red pin/pivot together at the same speed.

In reality the black weight doesn't just transfer its connection to the red pin/pivot - it loops around it [because the pin/pivot has a small diameter] - this means the black weight will spiral inwards & increase its speed as its effecive radius decreases i.e. the string winds around the pin again & again - so the black weight will pull ahead [comparing to a radial line] of the red weight circling its pivot [co-located] & its linear velociy will increase to above the red weights due to CoAM, IINM.

The black weight should actually maintain its speed. It's angular velocity around the center of the pin, however, should increase as it moves closer to the pin, so your "comparing to a radial line" seems to be correct. Also, the black weight spiraling inward actually loses angular momentum relative to the center of the pin in this case, but again while maintaining its speed.

So, after some spiraling of the black weight, both the red and black weights should both still be moving at the same speed and have the same kinetic energies, but both will then be at different radii from the center of the pin and so have different angular velocities and different angular momentums around the center of the pin. ...assuming they were of equal mass, of course.

I believe that's correct.

When the weight is spiraling around a pin or pole, the force applied to accelerate the weight is not directed through the center of the pin or pole but rather tangentially to its circumference, so there actually is a change in angular momentum of the spiraling weight around the center of the pin in this case, but with no change in speed or kinetic energy. Due to the conservation of angular momentum for the complete system this means there should also be a change in angular momentum of the earth or whatever the pin is connected to, also, but due to the much larger mass, the change would be immeasurably small.

Dwayne

[zoelra]

Fletcher and Dwayne,

I composed the reply around midnight last night, and after a long day at work I wasn't running on all cylinders you might say. You both mentioned a critical detail that I left out, and that is the pin needs to be of negligible diameter, so in both cases (red and black weight), they would have the same effective pinned position.

Obviously I was trying to make the point that angular momentum is NOT conserved in the puck experiment and I included one way of looking at the experiment.

Here is another way to look at the experiment. More deductive reasoning. We know that when a rotating object is pulled inward to a smaller orbit, and angular momentum is conserved, the energy of the object increases, matching the amount of work done to move the object to the inner orbit. So hypothetically speaking, if in the puck experiment, angular momentum were conserved, it would imply that the energy of the puck would also increase, and so would its speed. So where would the energy come from? I don't see how a pin changing the direction of the puck would add speed or energy to the puck.

Sorry for rambling on guys, but I know of only one way angular momentum is conserved, and that is included in my earlier "proof" post on Sept 10 at 9:12am. However, I would love to see any graphical or mathematical models of any other ways angular momentum is conserved.

[rlortie]

Dwayne wrote:

Many here speak of "velocity" which, of course, is a vector quantity that has both magnitude and direction where they really mean to say "speed" which is a scalar quantity and would be the absolute magnitude of the velocity. Forces can, of course, change the velocity of a mass without necessarily changing its speed.

This has probably been discussed at one time or another, but bear with me!

IMO few of us comprehend the significance of the size of Bessler's wheels. If a twelve foot diameter (3.657 m) wheel is turning 26 RPM, has anyone ever calculated it's circumference velocity? What would this be in miles or kilometers per hour. I believe some will find the answer surprising.

Once the speed and size of the wheel is comprehended, think of the alleged report that one man was capable of stopping it while being lifted from the ground!

I am a runt! I stand 5'-8" (1.7272 m) tall, weigh in at 165 pounds (74.84 kg). I would be able to walk under the axle without stooping. Considering the velocity, inertia, and kinetics, could I stop this wheel without being thrown over the top regardless of its mass?

It is questions like this that drive me to build my research wheels at a minimum of six feet (1.828 m) in diameter.

Edit: I do not claim to be a mathematician or even like math, so you best check my figures:

Circumference of a twelve foot wheel: 452.39" (11.49 m)
Times 26 rev per minute= 11,762.39" (298.75 m)
Or; 980.18 feet per minute (FPM) (298.75 m)
Miles per hour; 11.138 (17.924 km)

Ralph

[justsomeone]

Just over 11 MPH?

[rlortie]

JSO,

As stated; do the math yourself to confirm my calculations. Most of the above numbers were acquired through a converter.

If I am correct, eleven miles per hour is enough to do significant damage to modern cars designed to protect the occupants from major injury.

Ralph

[Dunesbury]

Considering the velocity, inertia, and kinetics, could I stop this wheel without being thrown over the top regardless of its mass?

You can't disregard its mass and answer that question. We have this discussion going on in other thread. Dwayne did some calculations to get estimate of wheel mass assuming man in eyewitness testimony stopped wheel with single grab and his weight was about average and he wasn't thrown over top, of course. Testimony was he was lifted from ground. How much is not known.

Here is Dwayne's calculation post in thread:

http://www.besslerwheel.com/forum/viewt ... 808#126808

[zoelra]

@Grimer,

Since we are on the subject of rotating objects and angular momentum, I want to throw out an idea that may be of interest to you.

Say we have a weight at the end of a string and it is revolving around a pivot point. We know that when we pull the weight inward radially, angular momentum is conserved and the energy of the object increases as does its speed. The path of the inward moving weight is a spiral. After the weight is drawn in, if we cut the string, the object will move off tangentially in a straight line with its increased speed and energy. There is no net gain in energy since we had to do work to pull the weight inward, and that work equals the energy gain of the object. Nothing new here, just a recap.

This got me thinking about “Uncle’s Toy�. When the marble rolls into the funnel, moving tangentially around the opening, gravity begins to force the marble downward into the throat of the funnel, and the marble moves in a spiral path as it moves downward. So the question is, could gravity and the forced spiral path down the funnel produce the same effect as pulling a revolving weight inward radially (as mentioned above)? That is, could angular momentum of the marble be conserved? When the marble exits the funnel it is like cutting the string on the revolving weight. Now you have a moving marble with energy greater than it would normally have. Something to think about.

[pequaide]

Franklin Hu; challenges us to find a laboratory experiment that supports angular momentum conservation.  I have been looking again on the internet and there is none. There is no lab experiment that supports angular momentum conservation.

If there is an experiment proposed they always go into a philosophical description/debate and avoid the collection of data. They avoid data because it does not support their theory. The pin at 45 cm experiment is eminently easy and could be set up in minutes; yet it is not done.  It is not done because the data does not support their theory.

The Moon orbits a gravitational source. The Moon’s tangent speed will increase if it gets closer to the gravitational source; it will slow down if it gets further away. The point of rotation is a point between the center of the Earth and the center of the Moon; the Earth is the gravitational source.

With gravity making these arc velocity changes Angular Momentum is conserved.  If gravity did not make these arc velocity changes Angular Momentum would not be conserved. Angular Momentum conservation is not cause by the motion of the object itself it is caused by gravity.  Gravity makes the appropriate changes in arc velocity as the radius changes.

The puck on the end of a string is not in orbit. Orbit has one and only one velocity for a certain radial distance from the gravitational source. The puck can have any velocity. 

The arc velocity of the puck is not changed when its radial distance is changed.

The same formula that can be used to describe the motion of the Moon cannot be used to describe the motion of the puck.

Once Kepler had the formula developed for comets it would work for other satellites, such as the Moon; but it will not work for a puck.

[Grimer]

@Grimer,

Since we are on the subject of rotating objects and angular momentum, I want to throw out an idea that may be of interest to you.

Say we have a weight at the end of a string and it is revolving around a pivot point. We know that when we pull the weight inward radially, angular momentum is conserved and the energy of the object increases as does its speed. The path of the inward moving weight is a spiral. After the weight is drawn in, if we cut the string, the object will move off tangentially in a straight line with its increased speed and energy. There is no net gain in energy since we had to do work to pull the weight inward, and that work equals the energy gain of the object. Nothing new here, just a recap.

This got me thinking about “Uncle’s Toy�. When the marble rolls into the funnel, moving tangentially around the opening, gravity begins to force the marble downward into the throat of the funnel, and the marble moves in a spiral path as it moves downward. So the question is, could gravity and the forced spiral path down the funnel produce the same effect as pulling a revolving weight inward radially (as mentioned above)? That is, could angular momentum of the marble be conserved? When the marble exits the funnel it is like cutting the string on the revolving weight. Now you have a moving marble with energy greater than it would normally have. Something to think about.

I've thought about it and made precisely the same point you are making that push is equivalent to pull. That the GPM is equivalent to the extended Milkovic which in turn is equivalent to an element of the BesslerWheel.

I'll have to see if I can find the relevant post(s).