Originally Posted by ExMachina
No. If the gradient is zero, an object in uniform motion (rotational or linear) will stay in uniform motion (minus frictional forces). The 100lb ball of lead may experience more ******ing forces due to friction becasue of its weight and the nature of lead (and therefore require more energy input to keep it going) but round objects of dissimilar weights, having similar coefficients of friction will be indistinguisable once they have been set in motion and achieved a set velocity.
The moment of inertia of a bicycle wheel is simple to calculate (I=mr^2, where "r" is the center of radial mass, not the radius of the wheel) and it works in *both* directions--just as it ******* acceleration, it also ******* decelleration. For all practical purposes, all bicycle wheels of similar weight and having similar tires will interact with the ground in the same way. Therefore, these same wheels will all experience idential ******ing frictional forces--regardless of how the weight within the wheel is distributed. Consequently, since a pair of wheels w/ different moments of inertia (ie, differing r's)rolling along at a constant speed CANNOT experience differing ******ing forces, they will therefore require EQUAL ENERGY inputs to maintain this constant speed.
Your explanation is very good textbook physics, except that forgot to factor in the decelerating effects of gravity (on hills) and wind resistance. The work required to maintain a perfectly even speed is equal to the work required to counter the decelerating forces of wind resistance and gravity. The previous sentence agrees with your explanation except when you put it into the real world of constant changes in velocity and rate of acceleration. If we could maintain a perfectly even speed, the weight of the wheel would not matter. But we don't. We are always changing our rate of acceleration. Because of this real world factor, the lighter wheel is more advantageous because it takes less work to bring back up to speed.
BTW, acceleration seems to have been misused a little in this thread. Not only is it a change in the rate, but it is also a change in the direction of movement. Therefore, the rim is always accelerating because of the change in direction of movement of any given location on the rim.