**Once and for all**
The key to understanding this problem is that the wheels can remain stationary in their own reference frame, but be moving in a whole other reference frame.
What is also key is understanding that the rate of the rotation of the wheels does not affect their displacement in a fixed reference frame.
Unfortunatley, the language with which the problem is being answered in is not the language which can explain the answer. mathematics holds the answer, and it cannot be explained through the words with which I write to you now.
However, for those that are struggling to get to grips with it, I suggest you consider other, well known and similar problems. Like Zeno's paradox (either the Athlete and the tortoise in a race, or moving towards a wall by stepping half the distance each time).
Or, you might like to try considering the sum of Geometric series where the r < 1.0 (i.e. adding 1 to 1/2 to 1/4 to 1/8 to 1/16 and so on...) What is the maximum this series can add up to? Infinity? No, it adds up to 2.
Lastly, you can try Lorentz transformations in the beginnings of Relativity.
All these problems share parallels with this. Counter-intuitive results, and that is why some people struggle to accept them, as they are contrary to everything they have experienced in their existence. However, given the correct tools and intelligent implementation, the answer can be proven a priori. Through mathematics. |