Yes. Airplanes produce thrust which pushes against the air around the aircraft, specifically air that is accelerated by its engine fan blades or propeller, and in the case of turbine powered aircraft, against engine exhaust (accelerated burnt fuel and air).
The airplane’s wheels rotate freely to allow the airplane to move along the ground with as little resistance as possible.
Sure. The wheels don’t provide any motive force, they just support the weight of the plane.
Try this thought experiment, instead of having wheels, the plane has an air cushion bag, just like a hovercraft. In that case the plane has no physical contact to the ground. It can be on a conveyor belt going 1000 mph, it would still take off
Yes. The wings only need to be moving through the air to create lift, and the engines push on the air to accelerate the aircraft. Even if it were on the treadmill, it would still be moving forward, the wheels on the landing gear would just be spinning faster than normal. In a strong enough headwind, the plane would be able to take off without even moving relative to the ground.
There’s a Mythbusters episode about exactly this treadmill question
The treadmill is irrelevant. The aircraft engines and wings interact with the air, not the ground. If a treadmill was running fast in the opposite direction, the wheels would simply spin faster as the aircraft takes off. Imagine that the wheels were skis and the treadmill surface was ice. The aircraft could still take off.
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