Speaking of rolling.
Some students and I were working on the problem wherein a rope is wound around a barrel to pull it forward. The rope pulls the top of the barrel as it unwinds. When you calculate the acceleration of the barrel, it is greater than would it would be if the rope simply pulled at the center of mass. This must imply that the friction force on the barrel pushes it forward, a surprising result to us at least.
Anything wrong with our analysis?