The engine makes the tire rotate a little faster... Similarly, braking causes the tire to rotate a little slower.
That's exactly what I have problems understanding. How exactly compute this "little faster/slower"? All I have is wheel axis torque, either positive when accelerating, or negative when braking. I still have no idea how to compute the "little faster/slower" value from it. Making up this value makes no sense to me as the slip value depends on it and the tire model depends on the slip value.