As the motor comes up to speed, the slip frequency approaches zero, and the rotor current becomes more resistive than inductive. That means its phase relative to the stator shifts by as much as 90 degrees. This picture shows the rotor current near synchronous speed:
Actually, no. There are two things happening here at the same time. The phase is controlled by the slip frequency: as the slip frequency goes from zero to infinity, the reactance of the rotor goes from pure resistive to pure inductive, which means the phase shifts through 90 degrees. The most favorable torque occurs in pure resistive conditions, when the slip is zero, and the rotor current flows in the middle of the strongest magnetic field.
But that's only half the story. As the slip frequency decreases, the effective rotor voltage also decreases, going all the way to zero when the rotor reaches sychronous speed. So although the phase angle is most favorable, the current is now zero. The current increases with rotor voltage, which is directly proportional to slip frequency.
Where is the optiumum? It's one of those typical compromise situations where the maximum torque occurs at a phase angle of 45 degrees, or in other words, at that slip frequency where the resistive and inductive components of the rotor reactance are equal. That's when the motor develops its maximum torque. It's funny that from my pictures, it appeas that the currents are pushing on each other more than they are pulling. (Remember that when it comes to electric currents, opposites repel.)
But as Colombo used to say, there's just one thing still bothering me. I have a nice set of pictures, with the relative phases of rotor and stator current going through 90 degrees over the full range of operating conditions...this lines up with the idea of inductance vs. resistance. But am I quite sure I'm using the right pictures? Here's another picture that suggests a different mode of operations:
I find this a very hard question, but there is one way I can look at it that makes me fairly confident of what is the right answer. Oh, I know I can supposedly do those "right hand rule" tricks where I point my thumb along the direction of current flow and curl my fingers this way or that, but really now. If you're relying on that kind of stuff to tell you what's happening in a physical situation, you're obviously lost. You really need to argue from physical realities, and it's not that easy in this case. I think I have the right answer, but I'm going to leave it for next time.