I honestly don't get this, why the force is minimum when you use the rolling constraint?
rolling is defined as a = rα
anything else isn't rolling
if you gradually decrease F (for a particular µk) until you get rolling, the minimum F will be when rolling occurs, ie a = rα
(hmm … or maybe we should increase F, and use the rolling equations, and find the value of F for which the friction equals µsmg ? )