Here is another not less interesting task: to train, say, from Leningrad to Moscow, are there any points that are relative to the road surface are moving back from Moscow to Leningrad?
It turns out that in every moment on each wheel there are such points. Where they are?
You know, of course, that the train wheels have a rim protruding edge (flange). And it turns out that the lower point of this region when moving train moved not forward and back.
It is easy to verify that, after such an experience. To a small circle, such as a coin or a button, stick wax match so that it is adjoined to the circle radius and far acted over the edge. If you set the circle to the edge of the ruler at the point and start to roll it right to left, the points F, E and D protruding part will move not forward and back. The farther the point is from the edge of the circle, the more they served it back when the rolling circle (point D will move in D').
Experience with a circle and a match. When the wheel is rolled back to the left, the points F, E, D protruding part matches happen in the opposite direction.
The point of the flanges of railway wheel move as a prominent part of the match in our experience.
You should not be surprised now that train there are points that do not move forward and back.
However, this movement lasts only a tiny fraction of a second; but, be that as it may, the reverse movement of a moving train still exists in spite of our usual ideas. Said illustrated by the figures below.
When the train wheel rolling to the left, the lower part of his protruding edge moving to the right, i.e. in the opposite direction.
The top shows the curve line (“cycloid”), which describes each point on the rim of a rolling wheel carts. Below is a curve described by each point of the speaker edge rail wheels.