Electrical – Why is the rotor power factor of the induction motor lagging

First things first there is something called Displacement Power Factor This is basically related to the phase difference between the voltage applied and the current drawn $$ DPF = \cos( \Theta ) $$ What this means for your case is if 10kW of real power is being consumed then there is 11.76kVA of apparent power (industry are charged based upon their VA consumption as oppose to W consumption hence why PF/DPF is important)

For linear loads and an induction machine will appear as a linear load: PowerFactor == DisplacementPowerFactor

For non-linear loads (rectifier-based systems etc) the disctinction between DPF and PF becomes important. PowerFactor takes into account harmonic distortion

$$ PowerFactor = DisplacementPowerFactor * DistortionPowerFactor $$ $$ Power Factor = \cos( \Theta ) * \tfrac{1}{\sqrt{1 + THD_{i}^{2}}} $$

So you can see for a linear load the THD = 0 and thus the DistortionPowerFactor = 1 and thus PowerFactor = DisplacementPowerFactor and is the cosine of the phase difference between the voltage and current

The problem is that the rotor and stator must have spaces called slots, in the iron for the conductors. The conductors and air in the slots have a lower reluctance than the reluctance of the iron. There are more slots than there are poles in the stator. The windings are distributed among the slots to form distributed poles. Their is a different numbers of slots used for the stator and rotor. Those two features prevent the rotor from becoming locked or "cogged" in the minimum reluctance position that would otherwise exist.

Even with proper selection of the number of stator and rotor slots, there can be reluctance variations at different rotor angles that cause torque fluctuations and inflections in the torque vs. speed curve. Skewing the rotor slots mitigates that effect.

Here is a picture of the rotor and stator of a 4-pole, permanent-split capacitor, single-phase induction motor.