Henry Ernest Dudeney/Modern Puzzles/Wheel Paradox Problems

Henry Ernest Dudeney: Modern Puzzles: Wheel Paradox Problems

The wheel shown in the diagram makes one complete revolution in passing from $A$ to $B$.

It is therefore obvious that the line $AB$ is exactly equal in length to the circumference of the wheel.

Now the inner circle (the large hub in the diagram) also makes one complete revolution along the dotted line $CD$ and,

since the line CD is equal to the line $AB$, the circumference of the larger and smaller circles are the same.

This is clearly not true.

Wherein lies the fallacy?

When a bicycle is in motion, does the upper part of each wheel move faster than the bottom part near the ground?

When a railway train is in motion, it is always the case that some parts of the train are travelling backwards.

Explain why.