# Finding the maximum force acting on a rolling tire

I have a problem where a lone tire is rolling, we may assume that the tire is a uniform disk. I need to find the maximum force acting on the tire as a function of friction if the tire rolls without slipping.

I need some guidance to solve the problem. I know that the force of friction is $$\mu mg$$ where $$\mu$$ is some friction coefficient (not sure which) and $$mg$$ is the normal force of the tire. I also know that the necessary condition for rolling without slipping is that $$v = R\omega$$, where $$v$$ is the velocity of the tire's center of mass, $$R$$ is the radius of the tire and $$\omega$$ the angular speed of the tire. I think I have to involve the torque of the tire somehow and use Newton's second law, but I am not sure how.

$$\mu$$ is the frictional coefficient for static friction since the tire is rolling without slipping. In the non-sliding case, $$\mu N$$ give a maximum value for the frictional force, not necessarily the actual amount.
• That's very interesting, thank you. As a follow up question, would it be correct to find the maximum accerelation of the tire by setting $ma = \mu N$? Or do I need to involve some other assumption on the wheel? Jan 12, 2021 at 5:47