Consider a small ferromagnetic substance like a small iron pin pointed on a table at the centre with a screw such that the pin is free to rotate. Now if a magnet is brought nearby the pin, the pin will get an attraction force towards magnet. If the magnet begins to rotate, the pin will also rotate accordingly provided that magnet moves at a uniform velocity such that neither it goes far from the pin nor the pin touches the magnet. So under these circumstances the pin will continue to rotate in the direction following the magnet.
This is similar to how an induction motor works. Here, there are two parts: stator and rotor seperated by an air gap. Now, when 3 phase supply is given (3 phasemeans 3 voltage waveforms of same magnitude but 3 different phases) in the stator conductors(coil), a rotating magnetic flux is generated (which can be proved mathematically). This is similar to the rotating magnet. As a result, this flux is cut by the rotor coils and an emf is induced. As rotor conductors are short circuited, 3 phase flux is generated by rotor to. Under the effect of two fluxes, as the stator is fixed the rotor begins to rotate. This is similar to the pin rotation under magnetic effect.
Note: It may come up as a question that if the pin get attached to the rotating magnet and then both rotate simultaneously what can we say it? The answer is it would be called a synchronous motor. In practical motor it can be done by supplying dc excitation to rotor with 3 phase supply to stator.
One can try this out by taking a slip ring induction motor and supplying 3 phasesupply to stator and short circuit rotor conductors. As a result the machine would begin to rotate as induction motor. Now, with the help of a changeover switch, connect any two rotor terminal to dc supply. The machine will behave as synchronous motor. But there remains few restrictions too under load conditions which I am not adding here.
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