Context: I am building a cart with mass m (including the cart and the payload) that has 4 wheels. The 2 back wheels will be driven by motors. I am trying to determine the minimum amount of torque motors need to supply to the back wheels so that they starting rolling (not spinning or in other words rotating stationarily) from rest, moving the cart forward
My current thought process: Motor applies a torque to the wheel, the wheel in turn generates a force onto the road surface which, in return, applies an opposite and equal force onto the wheel surface. This F_friction (road on wheel) causes a counter torque opposing the motor torque (FBD is in figure 1)
So with reference to a block sliding on a surface (figure 2) where one needs to apply a force that exceeds maximum static friction for the block to start moving forward from rest.
My question is, is it the same thing for the wheels where the motor needs to supply a torque that exceeds the torque caused by F_friction (road on wheels)so that angular acceleraton can increase angular speed of the wheels from 0 (at rest)? This also leads to another question. When the wheels have gained a certain angular speed, how do we know if they spin (rotating stationarily without moving foward) or roll (rotating and moving forward)?
All the questions above lead to my final confusion, is the condition (motor torque exceeds torque caused by F_friction (road on wheels)), that helps the wheels gain angular speed from rest, the very condition that causes the wheels to spin (or slip, term used by many people) instead of rolling? Can anyone help me with some thoughts on my analysis so far and derive equations to determine the minimum amount of torque? Thank you.