I often like to do thought experiments while #cycling and sometimes I can’t think all the way through to the end of the answer. Here’s a recent one for #physicists who specialize in #relativity. A #bike's #wheel rotates such that the bit in contact with the #road is instantaneously at rest with respect to the #ground (no skidding), at least in #NewtonianMechanics. On the other hand, the bit diametrically opposite to it is moving at precisely twice the speed of the #bicycle...
As if by magic, Wikipedia has an animation. My conclusion seems to be wrong and probably has something to do with Lorentz contraction as the fastest moving parts of the wheel approach c.
@inkynibs I think I'm trapped in thinking in Galilean transformations and not in Lorentz transformations and I suspect that some odd distortions will take place.
Now, imagine a #cyclist with the speed of #Hermes and the strength of #Heracles who can go as fast as possible but within the confines of what we know about the real world. If the above still holds, about the #tyres of the bike, then, in the limit, the top of the wheel can go no faster than the speed of light, c, and the mass of that bit of the wheel increases without bound. Does that mean that the bike itself cannot exceed c/2?
@mkwadee
Yup, assuming the wheels roll without slipping. But well before that point the bicycle will reach orbital velocity, so the rider won’t get any traction to accelerate . And well before THAT the rider and bike will be heated up by air resistance into a burning meteor.
@ThreeSigma Of course, that will apply to any wheeled vehicle. Supposing you could create enough down force to stay on the ground, you'd also be bombarded by dust particle moving at relativistic speeds which would probably act like cannon balls as their mass would be huge.
@mkwadee Again, classical speeds would still be deadly. If you did it on a tiny, supermassive, airless planet, you would also want to be sure the surface was totally flat, because hitting a bump would likely initiate fusion.
Another issue is how strong the spokes have to be to survive the centripetal force they apply. If made of known materials, the wheels would explode at some point after they catch fire.
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