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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.

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$\mu$ 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.

These links may be helpful:

  1. https://www.sciencedirect.com/topics/engineering/rolling-tyre

  2. https://www.jstor.org/stable/44562957?seq=1

  3. Frictional Force of a Rolling Object

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  • $\begingroup$ 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? $\endgroup$
    – StannisBa
    Jan 12, 2021 at 5:47

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