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Does the sprinter and the endurance athlete require the same cadence?
No. @xavierdisley is your man for exact numbers, but generally the longer the race, the lower the cadence. Once you get past a kilo, though, the range isn't huge. Somebody who rides pursuits at 110rpm might drop down to 90rpm by the time they get to a 100 mile TT
It's not possible to say what average cadence people ride at. It just covers too much variety in cycling.
It is possible to have a good idea what cadence humans should ride at... and it's around 90 - 100. Most regular/keen/trained cyclists probably average 85 - 95. Mountain bikers, racers and the talented often average a bit higher I reckon.