Consider a ring with string wound upon it, on a rough surface with $\mu$ enough for pure rolling. If we pull the string tangentially with force $F$, in which direction would the frictional force be?
Let $f$ be the frictional force taken along the positive $x$ direction. Let the mass be $m$, and the inertia around its center of mass be $I$. Then if $a, \alpha$ are the translational and angular accelerations respectively, then we should have $$ma = F + f$$ $$I\alpha = Fr - fr$$ $$a = \alpha R$$ where the last equation comes from the fact that the point of contact must be at rest.
From these equations I am getting $f=0$. So I think there should be no frictional force. Am I correct?