The electromagnetic field is rotating. If you graph the voltage of any phase against the amperage, (instead of against time, as you usually see it) you will see a circle - the voltage increases, reverses, goes negative, and meanwhile the amperage thru the windings ( thus the magnetic field)
follows.
The output of a transformer will rotate likewise, but not the transformer itself - unless the output windings are mounted on a shaft, nothing will rotate.
';squirrel cage'; is one of the arrangements used to get the motor started turning. ( another is capacitor) I believe the squirrel cage arrangement is used on small single phase motors, with moderate loads. I don't think three phase motors need any starting arrangement - don't know.
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