[COLOR=var(--text-lighter)] The whip would be a system with joints of an infinite resolution (or in this case, no joints at all).[/COLOR]
For me, i think of the whip as having a large but (crucially)
finite number of joints/levers (presumably the molecular-level connections within it). I think that we can learn something about how a whip transfers momentum by thinking about fewer and longer levers. I don't think that a whip would work if it truly had an infinite number of sections of zero length, because i think the rotation of levers with a non-zero length is the key thing.
I'm writing a much better-explained article on this, but here's a short explanation of what I'm thinking that the more technical folk on here should be able to understand.
Imagine this stick \ moving left to right across your screen, and then the bottom of it hits a barrier so it rotates to this / instead.
\\\\\\\\\\./
The centre of mass is about halfway up the rigid stick, well away from the point of contact, so the stick overall won't actually be slowed down much, it'll just go into rotation. But think what that means - if the stick as a whole (in particular it's centre of mass) is travelling roughly as fast as before, but one end has stopped, then the
other end must be going faster than before! (Being further away from the point of rotation means it has a larger circle to traverse, in the same amount of time.)
For me, this is the key idea. If now we consider a series of levers connected to each other, and one of them rotates, then the far end of that lever will accelerate and will be
pulling on the next lever in the chain. This is how momentum is transferred, and speed increases, along the whip (or along the throwing arm, though with far fewer levers). Each 'lever' pulls on the one behind when it rotates, which in turn pulls the next, etc etc.
Now, because each link rotates, it's all very non linear. If we imagine each link starts off horizontal (ie at the top of the loop, in that nice cartoon) and flips right over, 180 degrees, to be horizontal again (the other way up) then the very first 'pull' on the link behind that one is
up, not forwards. And of course that pulled link is itself connected to those behind it, so the whip curls and curves, with links much further down the chain being pulled into the loop of the whip and doing some funky things well before it's their 'turn' to rotate. There's lots going on.
But for me the overall mechanism is that a rotating link in the chain accelerates the ones behind it (which, equal and opposite, decelerate that first link) and so as fewer and fewer links remain in motion, the speed of the later ones goes way up.
People often talk about momentum being conserved and applying to a smaller and smaller mass of remaining whip tip - which is of course correct, as far as it goes. But I've not really seen anyone describe exactly how the momentum is transferred from one place to the next. This rotational idea is my thinking, and why i think the whip analogy is more true than most people actually think. Everything is levers and rotation, even a whip.
Thoughts?