I'm working on a design problem, and I'm having trouble figuring out how to model the torque needed to drive a bike tire at a set acceleration.

Let's say I have a tire with normal force between tire and ground Fn, coefficient of static friction between tire and ground u, and diameter d.

What is the necessary axle torque to drive the tire at desired linear acceleration a from standstill without slipping? How great can a be if you want to avoid slip?

Also, the problem doesn't give me a tire mass or moment of inertia. Is this problem possible without those?


1 Answer 1


Assuming the road level, because no information on slope is given, the maximum force before slipping is $F_{max}= F_n* \mu =mg\mu $

Then the torque will be $ \tau = mg\mu D/2=I \alpha$

assuming the mass of the wheel is concentrated at the perimeter its

$$ I= mD^2/4 $$

$$\alpha = \frac{mD^2/4}{mg \mu D/2}$$ $$ \alpha=<\frac{D}{2g\mu} $$

  • 1
    $\begingroup$ I think $F_n$ should be $m*g$, not just $m$. $\endgroup$
    – am304
    Feb 25, 2019 at 13:01
  • 1
    $\begingroup$ @am304, yes you're right. I have modified my answer. $\endgroup$
    – kamran
    Feb 25, 2019 at 16:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.