From the DT thread:
Originally Posted by makeinu
Well, the spinning wheel does affect translational motion because the bicycle (by its very purpose) couples the rotational motion of the wheel to the translational motion of the bike. I know you want to consider the physics of the translational motion by itself, but the translational motion does not exist by itself with a bicycle.
You are quite correct; however it is possible (and in fact simpler) to treat the 2 different kind of motions entirely separately and add the effects at the end, like in the OP. E.g., you can picture a moving bike as a bike with stationary wheels sliding along, plus a stationary bike with spinning wheels.
Originally Posted by makeinu
Also, I think it is a little misleading to say that only the acceleration is affected by the rotational mass. In an ideal physical sense this is true, but in an ideal physical sense all the energy put into the pedals will result in acceleration. However, the bike will slow to a halt if the rider stops pedaling. So it is necessary to "reaccelerate" the wheels to compensate for deceleration due to other factors. I'm pretty sure the smaller wheels will increase the efficiency of this process, even though the actual speed of the bike is not increasing, but I'm not that kind of engineer, so perhaps you can clarify.
Only a tiny tiny bit misleading: If a wheel rotational speed is constant, then there is no additional effect and I am 100% correct. However, as you pedal, the torque is not constant so there is in fact a small variation in speed, which is a small positive followed by a small negative amount of acceleration. This effect is larger when you ride up a very steep hill. So in that case I am indeed a tiny bit misleading.
I suppose this could be the reason why spinning with as constant a torque as possible is harped on a being best - you minimise those tiny accelerations.