Train Motion: Does it Really Move While Rotating Wheels?

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A train moving west at 50 km/hr has a wheel that rotates, causing the top of the wheel to move east while the bottom moves west. The bottom point of the wheel only moves if it is not sliding on the track, while the center of the wheel moves at the same speed as the train. If the velocities at the top and bottom of the wheel are equal, the train would not move forward, merely spinning its wheels. However, if the speeds differ, the train's movement is determined by the difference between the two velocities. Therefore, the train does indeed move, as long as the wheel's motion is not perfectly balanced.
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A train is moving west at 50 km/hr. In relationship to the tracks, the top point of the trains wheel is also moving east. However, the bottom point of the wheel is moving west. Assuming the wheel rotates at a constant speed, does the train really move at all?
 
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If the train is moving west then the top of a wheel is also traveling west but at twice the speed of the train. The bottom point of the wheel is moving neither west nor east unless it is sliding on the track. Of course, the center of the wheel is moving west at exactly the same speed as the train.

I can assure you that the train does move! :)
 
What Tide said, plus:

If the top of the wheel is moving east and the bottom is moving west, then no, the train does not move; it just sits there spinning its wheels. This of course assumes that the westbound velocity at the bottom and the eastbound velocity at the top are equal. If they're not equal, then the train moves at a rate equal to the difference of the two.
 

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