AscenXion, since Kington’s explanation isn’t enough for you, and you didn’t take the time to read and understand my previous post, I’ll give this one more go.
First, energy has nothing to do with any of this problem. Leave that behind. Yes, energy is conserved, however we’re not describing closed systems, so while the energy is conserved, if it’s radiated off in heat, it may as well be a non-conserved quantity as far as the rider is concerned.
Circular motion is an accelerated motion, you are very correct with that. HOWEVER, if the wheel is balanced, it does not take any extra force to maintain the rotation of the wheel, because the spokes provide all of the centripetal acceleration required to keep the tire moving in a circular path. Since the centripetal acceleration of a piece of tire on one side of the wheel is exactly equal and opposite in sign to the acceleration of a chunk of tire on the other side of the wheel, the NET ACCELERATION is zero. Thus, the net force on the system can remain zero and yet the wheel will continue to spin (assuming no friction).
Caveat: AscenXion is correct when he says that there is a mass term there. If we were concerned about whether or not our spokes would be strong enough to hold the wheel together at high speeds (a serious consideration when making things such as jet engines), then we would want to minimize the mass at the edge of the wheel, since more mass requires more force to accelerate. Thus, as AscenXion said, the centripetal force would be greater.
BUT, once again, NONE of the above has anything to do with the rideability of the wheel! The problem is one of angular momentum (refer to my previous post, and actually read it), and has nothing to do with centripetal forces (which really don’t come into play until you start trying to solve two-body problems like planetary orbits).
SUMMARY: Energy has nothing to do with this problem. Centripetal force DOES have a mass term, however centripetal force has nothing to do with the stability of the wheel and everything to do with the tension of the spokes. The problem of wheel stability when riding, etc is one of angular momentum. Read the freakin’ wiki or something if yous till don’t follow.