Is the formula of the angular momentum conservation wrong?

[cloud camper]

OK Fletch, I haven't tried the sims yet but you are no doubt right.

If you had time it would be helpful to hear an explanation why KE increases
but AM does not when weights are moved closer to COR.

Thank you for your efforts.

[cloud camper]

Cloud:

Then I confused you with the term “internal GPE field�.

This is the same vertical PE field (mgh or mass x gravity x height) that is experienced in an inertial (non rotating) reference frame except that it exists only within the boundaries of the rotating system.

If all mass is placed at the rim there is no internal GPE as the height is zero. If all mass is located near the COR but has the capability of migrating to the rim, the energy would then be described something like mgh as it has a potential relative to how far in from the rim it is located during rotation.

That is interesting CC, is that a concept you developed? Is it named something different or where can I study it more?

Thanks Dax - I believe it is interesting as well.

I am completing PPA application in a couple days (it's only $150) then can discuss my wheel concept in more detail but basically the idea is to create the internal GPE in place at essentially no cost before the wheel is spun up using an external descending master weight, then convert the internal GPE to KE while the wheel is spinning, spin the wheel down again as the AM remains constant using the same momentum to raise the external master weight once more.

We only want to extract the internal GPE, and not remove any energy from the AM field as that is conservative.

The extracted GPE is removed in a pulse like fashion, similar to an IC engine. These pulses can then be used to power a separate ratcheting flywheel (converted bicycle wheel with freehub).

A small amount of power (hopefully) is then extracted from the spinning flywheel to keep a clock spring wound that then powers an escapement wheel that restores lost energy due to friction and windage losses in the
oscillating master weight.

Will it work? I don't know. Is it the Bessler wheel? I don't know but all components can be sandwiched compactly into a small disc shaped enclosure.

But we do have weights gaining force from their own swinging and impacts as the weights collide with the rim. But the impacts do not power
the wheel.

I don't like to use the term CF as it is not CF creating the energy. CF only converts the previously created internal GPE to KE which is then extracted.

The whole idea with this wheel concept is to utilize the freely created internal GPE rather than bleed off the conservative AM.

[Dunesbury]

If mass of object is constant, to make both sides of equation remain equal, if velocity increases, either because of external force applied or internal force applied, then other side of equation increases.
KE = ½mv²
For rotation, m is moment of inertia and v is angular velocity.
Does that help?

[zoelra]

CC,

In the 2nd drawing I attached in my earlier post (Inward movement), an external force has to be applied to the revolving weight to overcome its CF and move it inward. As the weight moves inward in a spiral fashion, it's velocity increases according to the formula rv = RV. Angular momentum is conserved. The external work done by the force (the energy expended) to move the weight inward is converted to kinetic energy in the revolving weight.

Likewise, if the revolving weight is allowed to move outward under its own momentum, its velocity decreases by the formula rv = RV. Angular momentum is conserved, but the energy of the revolving weight decreases.


When you think of pumping weights in and out in a rotating environment, it can be a lose-lose scenario. First you lose the kinetic energy in the weight as it moves outward, then you have to apply a force (add energy) to move the weight back inward. The only way to break even is to collect ALL of the energy of the weight as it moves outward, then re-apply that energy to move the weight back inward. Good luck to anyone trying to use this process to gain any free energy.

[cloud camper]

Z - yup, I agree with that.

That's why I believe the wheel must be spun up and then brought to a stop repetitively using an oscillator mechanism.

In this way the weights can be freely repositioned near the COR to repeat the cycle (my opinion unconfirmed)

[Fletcher]

OK Fletch, I haven't tried the sims yet but you are no doubt right.

If you had time it would be helpful to hear an explanation why KE increases
but AM does not when weights are moved closer to COR.

Thank you for your efforts.

Hi CC .. ironically this was the same mistake jim_mich made in the original thread discussion that Wubbly pointed to [no jab intended].

Zoelra has explained it well, especially if you follow his vector diagrams.

Wubbly's spreadsheet was showing the same thing but using Calculus - follow it thru carefully, going from increment to increment, & you will see that he analyses it using linear terms & then cross checks using rotational terms - they match up for both inward & outward movements - it's very conclusive IMO & I found it invaluable because I could then run the math against the sims, which gave identical results.

N.B. the spreadsheets considered the masses only, whilst the sims had by necessity a small mass attributed to the wheel background which very slightly distorted the findings in the output boxes.

Basically they showed the same results - if you let mass migrate to twice the radius under momentum (inertia/Cf's) you halve the tangential velocity [you loose the radial component of velocity & are left with the rim direction component] & the wheel speed rpm quarters as does the KE.

The reverse, where you add energy to shift masses inwards against Cf's, results in you doubling the tangential velocity, quadrupling the rpm & KE - this is mirror image of the above - it also shows that MOI is r^2 related & not r as has been suggested - if it were r then these calculus equations wouldn't be symmetrical & we could have excess KE is one direction or other.

N.B. All the while AM is preserved.

As has been said many times, there is no Conservation of Kinetic Energy Law - it is Conservation of Energy.

[cloud camper]

Thanks again Fletch - you're a gem as usual!

[zoelra]

There are two ways to look at the conservation of angular momentum.

[Grimer]

An interesting controversial approach:
http://sci.tech-archive.net/Archive/sci ... 00775.html

I read this and the link and immediately I came across this.

"What is mysterious about this situation is that the skater is not
adding any energy to speed up their spin. Just the act of closing
their arms somehow accelerates their body without any apparent input
of energy. Energy is absolutely required to increase the spin rate of
the skaters body, but where does it come from?"

It comes from the fact that pulling in the arms does work. One is acting against Ersatz gravity and increasing the Ersatz gravity potential in an analogous way that one increases the Newtonian gravity potential when one lifts an object off the floor.

[zoelra]

What mystery ... the skater is adding the energy. Chemical energy stored in the skaters body is used to pull in his/her arms (no differently than when performing any other activity such as walking, running, standing, etc.).

[Trevor Lyn Whatford]

Hi all,

I did say on the other thread that one weight would be different to the two weight experiment, mainly because the 2 weight experiment is in balance, the same with the arms of the ice skater arms, bearing in mind that this sort of experiment is the empirical tested experiment people keep telling me about, it does rock my faith in the empirical tested known physics, when it is clear to me and my own experiments that there is a lot taken for granted, and when it is found that in fact that empirical testing of known physics is not complete then it would be just a theory and not a fact. Also when he tried a mass on a string experiment there would be a lot more forces and there vectors at play so the results would not be the same.

While you are looking at the coat hanger experiment you might notice the vectors of the pull inward (a torque force) to the center is required to accelerate the mass, and a constant torque force is then require to stop batteries from flying outward, it kind of reminds me of the planetary orbits, and to me it show that constant work needs to be done to maintain orbiting mass. In short all experiments have not been done yet, and there will be a few surprises when they are, so good luck with your experiments.

http://www.youtube.com/watch?v=9MGQJar8 ... SM4lz2-aYw

http://www.besslerwheel.com/forum/viewt ... sc&start=0

[Wubbly]

Zoelra,
Your geometric proof is beautiful. I would have used r₁, r₂, v₁, v₂ instead of r, R, v, V but your version works too.

From the radius geometry: cos(θ) = r₁ / r₂
From the velocity geometry: cos(θ) = v₂ / v₁
Setting the two equal to each other you get: r₁ / r₂ = v₂ / v₁
which can be rearranged to be: r₁ v₁ = r₂ v₂
which is the conservation of angular momentum formula.

Multiplying both sides of the equation by the mass "m" you get:
r₁ m v₁ = r₂ m v₂
or
r₁ p₁ = r₂ p₂
or
p₂ = p₁ r₁/r₂

So if the mass moves to a radius that is twice as large, then the new tangential (linear) momentum must be half its original value.

It's a beautiful geometric proof, and if someone believes the law of conservation of angular momentum is wrong, then they would have to argue that the geometry is wrong, which would be a difficult position to argue.

Your last post using the rotational equations could also be written:

ω₂ = r₁² ω₁/ r₂²

And it's easy to see what happens to the angular velocity if the radius changes.

[zoelra]

Thanks Wubbly ...

I tried to keep the math as simple and clean as possible to make my point. I do normally use subscript notation however.

The law appears to be valid, at least when the movements/conditions are met. Maybe this will put the issue to rest.

[Trevor Lyn Whatford]

Hi Wobbly,

does your calculations take into account for the push in the direction of rotation the acceleration of the weight has on the frame? The coat hanger is also accelerated by the weight being pulled inward, at the moment the string is pulled the force and angular motion vectors change dramatically. The same happens to the frame when the sting is released but this is a push against rotation, so there would be a increase of KE transferred to the frame from the pull of the string.

Edit, the Experiment is flawed, and there is a need for a better experiment, like, running a 12 inch Experiment long side a 6 inch experiment with same measured energy input put into each frame at the axle.
Edit twice, one weight on each frame would also be even better.

[Wubbly]

Franklin's experiment is good enough to show the general principle.

It was discussed in the conservation of angular momentum thread identified here, and there's no need to beat a dead horse.

Some forum members accepted it and others didn't, and no amount of explaining was able to convince anyone to switch sides.