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?