What will happen when we separate one of the motor phases while it's operating at full load?

motor will stop and the overload relay will trip.

the overload will trip , but in case of no overload protection the motor noise will increase untill winding may damage

Now if the motor do have an over load protections the over load will tripe.

Put if there is no over load protection on the motor circuit the coils of the motor will be burnet and in that case they will need a rewinding.

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Tested this a while back.

assuming no OLR

Full load: will decelerate and stop.

No load: Keep on running at same speed. Same principle of2 phase starter for single phase motor.