Motor Theory

But in a Sterling cycle motor there is four phases and not three.

My answer above may seem to be off topic but it does make my point. Most three phase electric motors are induction motors, but there are other motor circuits you might have. You must know many other factors of the motor circuit and geometry to calculate the expected results. The forces, currents and voltages are of course established by the very cryptic collection of Physics equations assembled by James Clerk Maxwell. These equations and the information you provide allow an engineer/physicist to predict the magnetic field generated by the stator windings. But to know the force this will impart on the rotor from a theoretical analysis you must know the magnetic field generated by the rotor. The easiest to calculate is the synchronous motor that has a DC current driven through the pole windings of the rotor circuit. To calculate the rotor field generated by an induction motor one must know either which standardized set of squirrel cage designs one has or go through multiple iterations of Maxwell's equations to get a suitable set of equations. Tesla received his patent for the induction motor in 1888. Over the years the squirrel cage rotor design have been empirically optimized for a variety of different load conditions. NEMA listed many different styles but today the most used ones are the A,B,C and D rotors.

Few people have the patience or need to go through all of this mathematics. Most people just look up the motor torque capability curves from the manufacturer. I do not know of a manufacturer that theoretically derives these curves but possibly there is somebody. I expect that most empirically measured their motor responses once and spot check all products at key speeds and loads.

The torque of the motor is determined by the inertia of the mechanical load and the time it takes to run-up to speed.

AC motor output torque, at a fixed frequency, varies by the square of the voltage reduction. So for example at 50% voltage, the torque is reduced to .5 x .5 or 25% of rated, at any point on the torque-speed curve.

But how that relates to starting a LOAD is totally dependent upon the characteristics of the load and the rate at which you need / want to accelerate it. This is also part and parcel to the current requirements etc. etc. It is not simple, but there are tools to help you do it now.

Is this a classwork assignment or do you have a real-world issue to solve?