Relating Motor Torque to Vehicle Motion

[hp-p00nst3r]

This is more of a curiosity question rather than a homework question, and it has to do with how to relate the electrical motor torque to a vehicle's motion using Newton's Laws.

Now for a vehicle (say RC car) moving forward in a straight line, the forces that are acting on it are the gravitational and normal forces, along with the rolling resistance and the force applied due to the rotation of the electrical motor.

I can easily write the equation of motion here in this case where it's just the
applied force - friction force = mass * accel

However, another problem arises when I construct an FBD for the car's wheel. In the case for rolling without slipping, it is the friction force that causes the wheel to roll forward, but when rolling resistance is not negligible, I am not sure how that is shown on the FBD. There is also the motor torque now present in the problem.

All I'm trying to do is relate the motor's torque to the applied force of the vehicle, and the approach I've taken is with the use of Newton's Equations of Motion.

 

[Mu naught]

If I understand you correctly, you are trying to account for the friction the wheel experiences as it spins around the car's axle. In which case, this is simply the torque produced by the friction in the opposite direction of the torque applied by the motor.

 

[hp-p00nst3r]

What about if the wheel was rolling WITH slipping? How would the friction force in the slip be modeled in the FBD? I'm not even sure if that is even a reasonable assumption. Pretty much everything that I've learned about rotating bodies in terms of friction has had to do with rolling with slip.