Conservation Of Angular Momentum (COAM)

[Stoatstail50]

You had it right in this 10 year old ad nauseam discussion about COM governing loop propagation.

This is an example of conservation of nauseam in a thread, which, because that particular thread ended, meant that nauseam wasn't conserved. Unfortunately, nauseam may yet be proven to have been conserved somewhere in another frame of reference for a bit...and then popped up again in this one.

[Paul Arden]

linear momentum is not transferable to angular momentum.

Are you talking about the real world or mathematical modelling Paul?

I’m not talking about anything; this is your chaps’ domain. I’m trying to understand!!

[VGB]

Not my domain either Paul, I am an engineer not a mathematical modeller. I want to see answers that are useful in the real world.

You cannot convert linear momentum into angular momentum because they are different properties. However in Gordys video, the truck has linear momentum if it does not collide with the rotor arm. But if it does collide with the rotor arm, it doesn’t have linear momentum.

Since we do not have collisions in a fly line, conceptually the discussion is pointless. You can’t have your penny and your bun.


The thread was started by Graeme asking a question:

Please explain COAM in the loop to me. I'm interested in your thoughts.

Presumably based on this post:

https://www.sexyloops.co.uk/theboard/vi ... 170#p75781

I think the conservation of angular momentum (COAM) is at play in answering that question. Angular momentum is not strictly conserved since there are outside forces acting on the loop (force from rod tip on the bottom of the loop and mass times acceleration and fly leg drag forces on the top). However those forces are close to being equal so the net torque on the loop would be close to zero and thus the angular momentum of the line going around the loop should remain about the same.

There’s been some dancing around the topic but appears to be no consensus which seems to be the end result of most physics threads. I’m going to reread Schmidt book again and page mark it this time, there’s a few bits I want to go deeper in.

[gordonjudd]

linear momentum is not transferable to angular momentum.

Paul,
You must have been paying attention when watching that video. He was very explicit in stating that linear momentum, p=mv, cannot be directly converted to angular momentum, L=rxp.

It is the equivalent angular momentum of the mass that is traveling in a straight line with an linear momentum value of p=mass*velocity that is involved in changing the angular momentum of the pivot arm.

It is necessary to compute the L=rxmv cross product to get the equivalent angular momentum (L) of the cart. That cross product involves a sin(phi) term where phi is the angle between the r vector and the momentum vector mv. This means the angular momentum of the cart will be equal to L= d*p where d is the nearest distance of the cart path to the reference point. That is why when he increased that distance it increased the angular momentum of the cart and caused the pivot arm to rotate faster with the larger d distance than it did with a smaller one.

Gordy

[gordonjudd]

I want to see answers that are useful in the real world.

Vince,
Will explaining how the diameter of the loop would be expected to change when a section of line with a different linear mass density goes around the loop fit into your real world criteria? It does to me.

If we take the relevant parameters of the cast with the Tenny TS-450 line into account we would expect the diameter of the loop when the heavier line line goes around the loop to be r2=r1*sqrt((v1*\(\rho_{l1}\))/(v2*\(\rho_{l2}\))). That equation assumes that the angular momentum will remain constant since the drag losses on the loop would be small and thus there will be no significant torque component applied to the loop to change its angular momentum.

Plugging in the relevant values measured in that cast we get
r2=.278*sqrt((11*.00095)/(11.37*.00318))=.149 m.

The measured value was .146m which is within (.149/.146=1.0205) 2% of the expected value.

That may not be close enough for you but it a useful prediction for me.

Gory

[VGB]

Gordy

We’ve talked about your ticking cast already, please can you answer this one?

To add context can you draw your centre of rotation and pivot arm on this idealised loop?

We can come back to your disagreement with DrPerkins on the loop velocity field

Vince

[Paul Arden]

Since there is no consensus on this topics, maybe it would be useful if someone would explain how they think AM impacts the cast and why or why not COAM does or doesn’t apply (and I have read James’ post carefully!!). And then others can agree or disagree.

That might save us going down too many rabbit holes.

Thanks!!
Paul

[gordonjudd]

We can come back to your disagreement with DrPerkins on the loop velocity field

Vince,
Just change the rotation center to the middle of the circle (that was my rotation center)_and see what you get. Dr. Perkin's and I do not disagree, we just used different centers to compute the v=omega*r values.

Gordy

[Graeme H]

Do you have a plot of the loop velocity that shows whether its magnitude increased or decreased during pull back?

Three plots in an earth frame, positive displacement to the left in the plots to make faster velocity a higher number. (Note: the frame rate of the video on the phone was 240 f/s but I don't know if that has been retained in the video after I added the contrast and clipped the time. Actual velocities might be wrong, but are internally consistent.)

Blue = Mk1, a mark on the rod leg showing when I pulled the rod tip back to the right (-ve direction)
Red = Loop nose
Green = Mk10, a mark on the fly leg 1 metre from the nail knot.

All plots have a node that is highlighted at this point in the progress of the loop.

This mark is on the rod leg and the highlighted node is 50 milliseconds after I initiated pullback (at 650 ms)

Turbo_Loop_Mk1_Vx.jpg (58.95 KiB) Viewed 102 times

Note the velocity of the loop has more than doubled during this video, after initially halving during the pullback.

Turbo_Loop_Loop_Nose_Vx.jpg (59.71 KiB) Viewed 102 times

Loop velocity in an earth frame can be increased by adding tension (by pulling back on the rod tip.)

Note the velocity was initially 20 m/s and increases to 55 m/s just before it enters the loop.

Turbo_Loop_Mk10_Vx.jpg (58.96 KiB) Viewed 102 times

To answer your question Gordy, the loop nose velocity does decrease while I am pulling pack on the rod leg. It then increases to well above the original velocity as my acceleration of the rod leg slows at around the 1 second mark (i.e. when the speed of my rod tip levels off, the loop speed rockets to a much higher velocity than it started out at.)

Interestingly for me, while that loop speed is decreasing, the fly leg speed is actually simultaneously increasing relative to the ground. It's not a zero-sum equation, where the fly leg speed relative to the loop nose remains constant. The plot below shows the mark on the fly leg has an increasing velocity in a moving frame of reference based on the loop nose.

Fly leg velocity relative to loop nose

Turbo_Loop_Mk10_Vx_Moving_Frame.jpg (55.39 KiB) Viewed 102 times

Cheers,
Graeme


(Here's the video if you want to see it in action.)

[Graeme H]

This is an example of conservation of nauseam in a thread, which, because that particular thread ended, meant that nauseam wasn't conserved. Unfortunately, nauseam may yet be proven to have been conserved somewhere in another frame of reference for a bit...and then popped up again in this one.