So...about that plane on the treadmill...

Incorrect.
You're missing a force in there.

Picture this:
Lay a tire on it's side on a frozen lake (close enough to frictionless for
this
example). Now wrap a rope around it a couple of times (like you would to
start an old outboard motor on a boat). Now quickly pull on the rope at a
tangent
to the tread.
You'll see two things happen.
1) the tire will rotate (Ok, that's pretty obvious)
but also
2) The center of the tire will move in the same direction that you are
pulling
on the rope.

The reason that the center will be displaced from it's original location
is the
same reason that the plane WILL move.

Your statement would be valid only under one condition.........If the
wheel, itself,
had no mass.


Hmmmm.. gotta think about that one. Not suggesting that you're incorrect but
just
wondering how the hub could act on the spindle if the bearing were truly
*frictionless*?!
Something has to push on something at some level. At what point are
frictional forces
described/replaced by more fundamental interactions? (maybe I need to
consult the great
oracle, wiki, to get the true definition of friction ;-)) On 2nd thought it
would seem that the
spindle WOULD be *pushed* backwards by photon pressure. (Holy crap! ... I
didn't want
to let THAT dead/alive cat out of the box.!) :-(

Also, by definition, the treadmill/conveyor will NOT MOVE AT ALL unless the
airplane/wheel hub
IS moving in the opposite direction. We're back again to the point of the
riddle which I believe
is to suggest that the airplane would take off regardless of what the wheels
or conveyor are doing.
(This is starting to sound more & more like the chicken and the egg.)

For Jose's question above, I think that by *frictionless* most people are
thinking of the hub &
bearings and not where the rubber meets the conveyor. If the wheel/conveyor
interface were
frictionless then neither the wheels nor the conveyor would turn unless the
problem can be interpreted
as the conveyor matching the hub's linear speed rather than the wheel's
angular speed. Either way
the plane takes off when it reaches sufficient airspeed.

Tony P.