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I was able to do that, but the problem I was having was that if the torque provided by the motor, exceeds the torque due to friction, the wheel will slip. According to our equation, our wheel will always slip. Since we want m*g*r = m*g*r*u (u=coefficient of static friction). U is almost always a decimal, meaning the friction force will always be less than torque force. What am i missing here. To go up a steeper hill, we need less torque? doesnt make sense.

I also tried to think of it in terms of energy and power output. Moving along the ground, the force over a distance, or work done by the motor must be more than the work done by friction. Also, when going uphil you also have to fight gravity, so it makes sense that steeper angles require more energy. However, I haven't been able to get much further than that.

Any help is greatly appreciated.