# How to resolve high coefficients of friction while rolling?

Static coefficient of friction is 1.6 between rubber and steel. Let's say you put a steel ball on a rubber incline at 45 degrees. Friction is more than gravity so it can't accelerate transitionally down the ramp. But there's clearly torque by friction * radius around the center of mass, so it has an angular acceleration. Also, it has to be nonslip motion because slipping only occurs with low coefficient of friction. However, this is a contradiction. How do you resolve this?

• Static friction is always less than or equal to $\mu_s \times$ the normal force. The static friction force is whatever is needed to make the ball roll without slipping, i.e. the angular velocity $\omega$ of the ball is equal to $vr$. If the friction coefficient is very small, it might be impossible to have enough static friction force to do that. In that situation, you have dynamic friction which is always equal to $\mu_d \times$ the normal force, and the ball will partly slide and partly roll. (The static and dynamic friction coefficients are always such that $\mu_d \le \mu_s$.) – alephzero Jan 17 '17 at 9:32