I agree now that my assumption probably wasn't the obvious one. A little deeper insight into why I made that assumption... It was the "exact same speed" statement. If I assume that the wheel's circumference and angular velocity represent the speed of the wheels. The wheels would then be skidding down the runway if the treadmill matched that speed. The wheels would only be rotating at half the angular velocity necessary to keep up with the planes forward movement. To avoid a skidding wheel, my brain assumed that the "teaser" part of the question was referencing a treadmill that would counter the wheels' rotation. Yep, convoluted.
Sorry my tone was a little crappy in the other posts. So could not another answer be that the treadmill is rotating clockwise to be opposite the counter-clockwise rotation of the wheels? This would mean that as the treadmill attempts to match the rotational speed of the wheels, the wheels start spinning faster, and the conveyor rotation and wheel rotational speed would approach infiniti, unless slippage occurred between the tires and conveyor belt.
Yes - the wheels would start to skid once the power from the engines overcame the adhesion of the tires to the conveyor belt.
The "speed of the wheels" could be understood to mean the rate they were spinning at, rather than the speed you mention here i.e. the speed of the plane. For example, if the plane were picked up and lifted down the runway at 5mph, the wheels would not be spinning at all, but you would say they were going 5mph. IMO you phrased the question unclearly, hence the misunderstanding.
Allow me to quote what you wrote earlier: "Example: Plane(and it's wheels) 75mph west Conveyor 75mph east Wheels *spinning* 150mph Plane airspeed 75mph" Looks like you were measuring circular actions in mph there. Aren't you contradicting yourself?
There is a problem of logic with this statement whatever speed achieved by the wheels is matched by the conveyor belt. and I cannot explain what. But plane would take off for the same reason that plane doesn't need the wheels to fly. Wheels, conveyor are irrelevant. Airplane engines generate thrust regardless of wheels. Think, if conveyor was able to prevent plane to take off, planes would never fly. Wheelchair uses friction against the ground to move. Conveyor would negate the friction. Airplane uses the air resistance (friction??) to move. Therefore irrelevance of conveyor belt.
Thinking about it. Speed is relative. It must be measured in comparison to something else. Obviously here, against the ground. Based on that, what matches exactly speed of wheel??? Fucking ground. So logically, conveyor is motionless in relation to the ground (if it matches speed of wheels) So guys, situation described is just the plane taking off nothing more nothing less.LOL.