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In response to John Mallinckrodt... I didn't necessarily want to imply
that "no dissipation of energy" is 100% possible. But I was saying this
in the same spirit that we say it when we study "elastic collisions" in
general-physics class. We still do that don't we? I.e. we pretend it
is possible to have an elastic collision, which is defined as one in
which kinetic energy is conserved, even though we know the deformation
of the bodies during impact will result in some amount of thermal
energy.
Is that where we differ, John? Or are you talking about something
else I am not picking up on?
Also, what assumptions are being made about I for this wheel. I was
assuming a disk with I = 0.5mr^2. In this case I get v_f =
r*w_0/sqrt(3) if there is absolutely no dissipation, and I get
v_f=r*w_0/sqrt(5) if there is dissipation due to "slippage."
Note that there is no disagreement that mu does not appear, and that
the final velocity is r*w_0 times some factor. We just aren't
agreeing on what that factor is.
I'm not getting r in this factor, I assume because of my assumption for I.
But also, is there a dimension problem in the results that John
gave? How do the units work out on the factor that multiplies
r*w_o? Doesn't that need to be dimensionless?