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> wheels of a bicycle rotate into the opposite direction Your example reminded me that on a very rare occasion something that sounds stupid and counter-intuiti
by alister 10y ago
> wheels of a bicycle rotate into the opposite direction
Your example reminded me that on a very rare occasion something that sounds stupid and counter-intuitive is true: A train wheel always has some point on it that is traveling backwards when the train is moving forward. It sounds ridiculous, doesn't it? If the train is moving forward, then all points on the train are moving forward. How could it be otherwise?
This is very difficult to explain without a diagram:
https://books.google.ca/books?id=SiviAgAAQBAJ&pg=PA143&lpg=PA143&dq=train+wheel+travels+backward++prolate+cycloid&source=bl&ots=E5JpPwNEcT&sig=tAzwZA1jY4cLsKv7l8DDre97FbY&hl=en&sa=X&redir_esc=y#v=onepage&q=train%20wheel%20travels%20backward%20%20prolate%20cycloid&f=false https://books.google.ca/books?id=SiviAgAAQBAJ&pg=PA143&lpg=P...
- deleted 10y ago[deleted]
- OscarCunningham 10y agoI think the thing with the train wheels is sort of obvious once you see that it only works because part of the wheel overhangs the rail. The axle of the wheel is moving forwards, and the bit in contact with the track is stationary, so the bit further out than that is going backwards.
- StavrosK 10y agoI don't think it's that difficult to explain. The part under the track, the "flange" goes backwards. The part exactly on the track is not moving at all, same as a car (or any other) wheel. This is also pretty obvious when you consider that if the wheel was turning in relation to the ground, it would be skidding.
- tgb 10y agoI can say with confidence that you're wrong about a point on a non-skidding wheel moving backwards. I can't read your book though, it says that the page is unavailable. Consider the wheel in the frame of the train. The train moves at velocity v relative to the ground. So the bottom of the wheel moves with velocity v backwards in the frame of the train. The top moves velocity v forward in that frame. All other points move at the same speed but in directions that aren't perfectly horizontal so move at a slower horizontal speed. But for a point to move backwards relative to the ground it must move at a horizontal speed greater than v in the frame of the train. So there is no such point.
- lotyrin 10y agoI haven't read this either, but the flange(?) of the wheel, the part below/behind the rail, is on the same lever as the point where the wheel contacts the rail (v), but further from the axis, so it's moving further (>v), also opposite the direction of the train's forward motion, so total negative speed, in the frame of the rail/ground. This is why a train is picked over most vehicles, which operate as you describe.
- tgb 10y agoYes, you're totally right, my analysis applies to bikes not trains! A tale in over-confidence / Google book previews availability.