The wheels movement would be driven by the belt, it doesn't matter which way the plane is traveling or on what surface, the wheels only move when a surface touches them so they will be driven by the belt - which according to the question, moves in the opposite direction to the plane.
I believe that in the end I misinterpreted "the opposite direction of rotation". Therefore I have new view, more or less what others have said and also my first thought. Forward motion of the plane is countered by rearward motion of the belt. In theory: The belt will increase speed into infinity, keeping the plane in place. In practice: The belt will soon reach it's maximum speed, limited by it's motor, the plane will move forward (with the wheels turning at normal plus belt speed) and take off. Tomorrow I will have a different opinion.
this is funny, I understand those that are yet to understand, you will get there, but funny part is how certain people are and then once they figure it out... Oh ****!
one of the best explanations so far. Simple and to the point. Really, the only question is whether or not lift is created. Without forward movement and/or wind, no lift is created, so no flight.
And now for something almost completely different: We all know an F1 car could drive upside down from a certain speed (eg against the ceiling of a tunnel. Putting the wings upside down could make it take off. Q: Could you make an F1 take off and land on it's wheels and how far would it fly. (Wings within regulation size) Have a nice weekend!
It depends on the speed of the car at lift-off and the weight bias front to rear. I think that without movable control surfaces the car would be susceptible to blow over or nose dive, much like the experiments with paper airplanes. It can be done but the flight characteristics change depending on how hard it is thrown (driven) and how it is balanced. It's an open equation because of infinite variables hence no need to discuss it further without more data or parameters.
The idea was with no movable control surfaces. I think it will lift off as soon as the speed is reached where enough lift is created (logically), but with the wheels not touching the ground it will not accelerate anymore but slow down quickly because of drag. And fall back to earth after a few meters.
Sounds good on paper but even with down force cars tend to blow over, Like this Mercedes at LeMans, http://www.youtube.com/watch?v=Ow3rxq7U1mA&feature=related , http://www.youtube.com/watch?v=SFN_Gp1eHN0&feature=related and this one, http://www.youtube.com/watch?v=BgYyP8YKsas&feature=related. With loss of thrust and no movable control surfaces their is no way to control pitch. Drag takes over and the car blows over.
Here's the skinny. The OP says that the conveyor belt is moving at the same speed as the airplanes wheels, but obviously in the opposite direction. Therefore, there is no forward progression of the airplane to create thrust and lift. So, the plane is actually remaining stationary and no lift off can occur. It's really simple dynamics.