Does a 700c wheel help you go faster? Someone suggested going with a 700c wheel to go faster, and after thinking about it I am wondering if a larger wheel actually does go faster. I understand that your gears will cause a wheel to rotate once and if the wheel has a larger circumference it will travel farther, but this comes at a cost to leg power, and why not just get a larger sprocket? So cut out the gears and such and talk about the physics.

I was lead to believe that rotating weight is what slows you down, so a larger wheel will have more mass, thus making it harder to push, hence slowing you down. A bike with 12" tires going the same speed as one with a 700c will have less rotating weight so will it be more efficient? If you are on a flat track with thin, hard tires and your bikes are geared to be equally efficient to pedal at low and high speeds, which wheel will make you faster?
The increased weight of the larger wheel (if indeed it does increase) will of course add weight to the bike, but additional weight adds very little rolling resistance (though it does of course affect hill climbing).

It is a myth that "rotating mass slows you down".  In terms of top speed there's no difference between weight on the wheel rim and weight anywhere else on the bike.  Added weight on the wheel rim does reduce acceleration, but 10 grams on the wheel rim only has the acceleration-limiting effect of 20 grams elsewhere -- it's not really enough to notice.  (And once you've accelerated to speed this effect goes away.)

A larger wheel can ride over slight irregularities in the road with less energy expenditure, and so can be more efficient (and less tiring) in some circumstances.  And a larger wheel generally is more stable (though at the expense of maneuverability).