Maybe this was discussed on the old board, but I'd like to re-examine the concept here please.
Most of the time when we discuss the physics of the loop, someone will raise the application of conservation of angular momentum (COAM) within the loop as an important aspect of the loop. In a recent thread, COAM was raised several times, with the implication that it is the conclusive evidence of physics within the loop and we don't need to go any further. Job done, physics settled.
In that thread, I was asked if I agree with applying COAM to a loop, and I replied with a firm "NO!", not elaborating because it was yet another distraction from the matter at hand. In the thread on Propagation of the loop 2 (another on physics) I asked the question about COAM to start a discussion but the thread quickly deviated before anyone answered it.
Can we please try to stay close to the topic of COAM in this discussion? I'd like a chance to get answers from those who adhere to this concept and I'd like to examine experimental data that we can now very easily capture and analyse within Tracker (rather than resorting to models.) This is a chance for you to educate me about why you think COAM is gospel. (In return, I'll try to avoid waves - unless absolutely necessary ...
)My understanding of the support for the application of COAM is that when the loop nose is chosen as the frame of reference, the velocity of line entering the loop equals the velocity of the line exiting the loop (opposite sign) and that within the loop itself, angular momentum is conserved as the line particles rapidly gain angular velocity around a centre of rotation thought to be somewhere within the centre of the loop.
That looks like this in Tracker when a line particle is digitised passing through the loop nose if the moving frame of reference is the loop. (Top graph is displacement, middle graph is velocity and the bottom graph is angular velocity.)
- Moving frame of reference centred on the loop (cast towards left of frame in video)
The presence of a high magnitude for angular velocity in the bottom graph is the support for the presence of COAM (as far as I understand the theory.)
Here's another project with a similar profile of velocities, but in another direction. (We can discuss this one later if required. Wither fewer data points, the data is a bit easier to use and replicate if someone wants to do that.)
Both screenshots seem to indicate that as the line goes around the loop, linear momentum is converted into angular momentum within the loop, where it is conserved and then converted back into linear momentum in the opposite direction.
I believe this is the summary of the concept of COAM. (If that's wrong, please elaborate.)
So why should I find that inconceivable? Because the same measurements using an earth frame of reference show that the particles of fly line have a velocity of zero in the rod leg. Zero velocity = zero momentum. Far from being conserved, the linear momentum of the fly leg is destroyed at the loop nose. At which position within the loop did the linear momentum of the fly leg convert from a positive value to zero?
- Earth frame of reference (cast towards left of frame in video)
If fly leg momentum is conserved as angular momentum within the loop, why wasn't it converted back into linear momentum as it left the loop?
To paraphrase a US politician, the loop is the place where fly leg momentum goes to die.
Further, the loop is not a point mass, which is the first requirement discussed in the video on Angular momentum posted by Torsten in this thread. The presenter says "... for the sake of this, we're going to assume it's a point mass ...". Without a point mass, it's impossible to use the loop as frame of reference. Momentum requires mass in addition to angular velocity. Yes, the line itself has mass, but it is constantly passing through the loop nose, each point mass of line leaving it as another enters the loop. It has no mass of its own, so there is nothing to track as a point mass for the purposes of analysis.
When we examine the Tracker video closely we can see that when line enters the loop, it has a slight downwards displacement shown as a slope rather than as circular motion. When the particle hits the loop nose, all forward velocity is lost (and thus momentum = zero).
I realise people are going to say "but the marker moves around the loop in a curved path! "Be very careful about hanging your hat on that. In the world that contains the fly line, the rod and the fish we cast at, the marker is just travelling to the left and down when it reaches the top of the loop. From that point in time, it's not travelling to the left any more.
Please explain COAM in the loop to me. I'm interested in your thoughts.
Cheers,
Graeme
