rene wrote: ⤴
Sun Sep 29, 2019 4:21 pm
I am afraid it really is tan(). It of course depends a bit on which angle we take as "the angle" as to how things work out exactly, but it'll never be sin(). Specifically for 45deg, V'=V is precisely right.
At 90 degrees, the top paper moves horizontally and the contact point moves at the same speed as the paper.
With tan(), V' -> zero as you get to 90 degrees; but try it with two pieces of paper: move the top one horizontally (angle =90 degrees) and contact point obviously moves at the same speed as the paper. Or try it at 89 degrees and you'll see that the speed is very close to the speed of the moving paper, but not close to zero.
The contact point never moves more slowly than the top paper.
Mind you, not meant as an argument-from-authority but only in hopes of communicating that I'm not merely guessing, I am trained as a mathematician.
Let me draw something and scan or some such and get back to you...
Edit: in my picture the original V direction is supposed to be
oriented in the same direction as the top paper, not the bottom paper, like an arrow drawn on the top paper and fixed to the top paper, but it looks like I drew it wrong (rotate and collapse image layers in the wrong order). I think this is why we're getting different answers!
Edit2: like this: