Frequency of stator current in induction motors
The rotor frequency is f_rotor = s*f_stator. You can see, that when rotor is in sync it has 0 Hz, no current is induced therefore no torque is produced.
The equivalent circuit of induction motor is similar to the equivalent circuit of the transformer. There is a transformation ratio in between stator and rotor, like the ratio of number of turns of primary and secondary windings in the transformer. A hint: the squirrel cage can be seen as single turn.