Correct, assuming the wheel is allowed to skid forward (as stated pretty far back, you may not have seen that post).
But, I was assuming the “spirit” of this constraint could not be overcome with skidding.
Once again, it all depends on the assumptions made.
I take it back, you are not correct.
I was thinking you were allowing for skidding, but I just realized you are saying something different.
If you want to understand why there can be no forward movement, do this little experiment at home:
Get 2 strips of paper, each 1 foot long
mark 1 as “wheel” - this represents the unrolled circumference of the wheel
mark 1 as “belt”
Place a mark every inch on both pieces of paper.
Place both pieces of paper next to each other so you can see the marks line up.
One end is considered the starting point and represents the contact between wheel and belt at time 0.
Place a mark on a stationary object next to the time 0 mark.
Move both pieces of paper past the stationary object in the same direction, at the same speed.
This was an example of wheel and belt at same speed.
Now, create your scenario where the wheel and belt are at same speed but the entire wheel is able to move forward.
Both of these conditions must be met, simultaneously:
1 - Same Speed At All Times
Marks on both pieces of paper must be lined up at ALL times. If at any time they don’t line up then they just moved at different “speed” according to our definition.
2 - Forward Motion of Wheel Relative to Stationary Object
After the last mark on the belt goes past the stationary object, at least the last mark on the wheel has not gone past the stationary object. This would represent net forward motion of the wheel relative to the stationary object.
As you can probably see, if you are able so satisfy #2, then you have just violated #1 and vice-versa. Either way, try the experiment if not convinced.
Let’s follow your analysis:
At this point the plane moved forward.
This means we have some airflow, good the passengers are happy.
Wait, what just happened.
We had forward movement and airflow just a second ago?
If we’re talking about a Harrier on a treadmill, then the answer is yes.
But I don’t think that’s that point of the question. It would be the same as asking if a helicopter could take off on a treadmill.
The treadmill under the airplane stopped the forward movement of the airplane.
If you have a kite you can get it off the gound by running and pulling it behind you. Try that on a treadmill. You would be running forward, the treadmill is matching your forward movement, but the kite would be on the ground behind you.
Part of my silly assumption of the OP was that the treadmill was itself on a treadmill going the opposite direction of the first treadmill.
And the second treadmill is on a third treadmill.
I think the third treadmill should be on a turtle. 
Now let me get the gist of this thread straight.
[ul]We have a magical treadmill able to instantaneously and continuously match the rotational speed of a wheel on it.[/ul]
[ul]The wheels we put on it feature magically frictionless bearings, treads with perfect traction and are attached to an otherwise pretty ordinary jet aircraft.[/ul]
[ul]Normally the thrust of the jet engines would accelerate the aircraft forward, eventually attaining enough airspeed for flight. In this situation all the thrust of the engines is converted into angular momentum of the perfectly frictionless wheels due to their necessary interaction with this magical treadmill. The aircraft never achieves a sufficient airspeed for flight [/ul]
So is what we have here is essentially equivalent to an effective set of wheel chocks?
Are the wheels rolling to begin with? The reason I ask is if they begin stationary with zero angular momentum and zero forward velocity relative to the treadmill, how do they begin rolling? Can forward thrust be converted to angular momentum without at least an initial displacement? Is such an initial displacement in conflict with the magical properties of the treadmill? Just how much magic we talkin here?
Are there relativistic issues? I thought briefly that once the treads reached the speed of light, no more angular acceleration would be possible, and at last our plane could take off. The treads of the wheels can never achieve the speed of light however; we can pour energy into them forever and due to relativistic effects they will continue to absorb rotational energy as their apparent mass increases. Perhaps if our wheels were magically massless our plane could take off?
Could we dupilicate all this without the treadmill and just another set of magical wheels for the aircraft wheels to sit on? Just in case we dont have enough mana for both wheels and treadmill.
Sorry if I missed any of this in the previous 360 some posts.
But the kite has rocket moters on it. You are now a moo point.
It all depends on if the tread mill can accelerate to the point to put enough friction on the landing gear, through the bearings or the tread contact, to overcome the force of the engines. Once the the wheels hit about 200-300 miles per hour, the whole thing is going to come apart.
I think what’s kept this thing going for a hilarious 7 pages is that the question being answered is not the OP. The question being answered is,
“Can you posit a scifi treadmill, outside of the laws of physics or rationality, that could make it impossible for an airplane to take off?”
The resulting thought experiment seems to have imagined a treadmill which manages to absorb ALL of the “equal and opposite reaction” of the jets’ or propellors’ actions.
Since this is not really possible, again I say the OP has been answered. The only way to believe otherwise, IMO, is to consider the OP to be a question along the lines of, “Is god so omnipotent that he could create a mountain that was too big for him to move?”
Um, duh-uh. This is a thought experiment. No one is planning on actually building such a treadmill. The nice thing about a thought experiment is that one can examine the various influences on a problem one at a time by reducing or increasing or eliminating other influences. Don’t like friction? Posit zero friction. Worried about high speeds? Posit infinite velocities. Works great when you’re looking to seperate out various effects.
Unless, of course, you miss the entire point of the exercise in a fit of giggles. Then it’s pretty useless.
I was kind of thinking the kite would have a couple Saturn 5 rocket boosters, the kite string is made of the finest Egyptian cotton, the treadmill is created of Siberian albino mink pelts and the runner is naked except for a ball cap and a half full enema bottle suspended from his genitals.
With that in mind I don’t see why it wouldn’t work.
It is possible that I was hasty and mistaken in my answer. Angular momentum does count. On the other hand, the energy that is turning those monsterous wheels is coming from the treadmill and not from the airplane, as Sam Stone noted. I still have difficulty seeing how the turning of the wheels would apply a linear force to the axle through a frictionless bearing.
In addition, the OP wasn’t imagining some outlandish monstrosity of an airplane for the test.
No, it is not wrong. People are continually bringing up automobiles and bicycles. There is no analogy between an airplane’s operation on the ground and those two. The friction between the automobile or bicycle tire and the ground causes the tire to roll forward on the ground and this pulls the verhicle along with it. The airplane doesn’t move this way on the ground. The propellor pulls on the air forcing the air backwards. The mass of air going backwards has momentum and this gives the plane an equal momentum going forward. Just exactly like an airplane wing gives a mass of air momentum downward and this allows the airplane to overcome the force of gravity and fly.
And one more time. The extra angluar momentum of the wheel does not come from from the plane. It comes from the treadmill.
I’ll stick with my answer in this post.
In the post I should add to “as long as the wheel bearings hold out” the words “and the tires don’t disintegrate.”
Please, answer the question about the bike. It will help you understand the problem.
The bike will slow down. I also understand that this hypothetical has nothing whatever to do with a plane on a treadmill.
Why bring up bicycles with their mode of ground propulstion sliding on ice or a pavement when the question is about airplanes with their entirely different mode of ground propulsion on a treadmill?
The bike slows down becuase there is a force from friction between the tires and the pavement that is transmitted through the axel to the body of the bike to the person riding the bike, correct?
Becuase its not as different as you think.
When an airplane lands part of its slowing down is a result of bringing the wheels up to speed. In this case the energy to speed them up comes from the plane. In the case of the plane on a treadmill, the energy to speed up the wheels comes from the treadmill. Or do you disagree with that?
Are they not as different because you say so, or is there some other reason?
No I don’t disagree but I don’t think its particularly relevent to this problem. Is what I said about the force accurate? The force from friction is transferred through the axle to the body of the bike and then to the rider. Since there is an unbalanced force on the rider and the bike they decellerate. Is that correct?
Because you disbelieve the fact that force can be transmitted through a bearing. This has nothing to do with where the energy comes from, or the mode of propulsion of the vehicle. It has everything to do with a simple force balance on the wheel.
You said: “force backwards on the wheels can’t be transmitted to the fucking plane.” That force has to be transmitted, otherwise the center of mass of the wheel is accelerated backwards. F=ma. Free body diagram.
Would anyone like to address the issue of the treadmill matching the wheel speed exactly?
If the wheel speed is matched exactly by the treadmill, how could the plane move foreward al all?
Anyone?