A tire of radius $R$ rolls on a flat surface with angular velocity $\omega$ and velocity $v$ as shown in the diagram. If $v>\omega R$, in which direction does friction from the tire act on the road?

The solution of this question can simply be understood by taking a situation of car driver, where at higher speed he applies sudden brakes, i.e. $v >\omega r$ and the tire rubs the road and we have rolling with forwards slipping i.e. friction acting in opposite direction of $v.$ (towards left in the above situation.) Friction force on the tire is towards right and on the road is towards left.