An induction motor is inherently self-starting
Why does a ceiling fan start slowly? [closed]
A much easier way to think about it is to consider energy. When the fan is spinning it has quite a bit of kinetic energy (try to stop it by putting your finger in the way to confirm this ( don't do this really!)). This kinetic energy is actually the square of the rate of rotation.
When the fan starts, the motor has to add energy. This is done by drawing energy from the power supply. Well, the amount of energy the supply takes per second is the power of the motor. If the fan is to start very quickly, it needs a lot of power while the fan is rotating. That means both enormous cables are required and the motor itself would be huge. As soon as the fan rotates, it requires much less power, so that all of this is only required during the startup process.
Economy and the desire not to have huge motors and cables attached to the ceiling, which almost certainly requires special support beams, possible liquid cooling arrangements, etc., lead to the fact that rather small motors are used and people live on spin-up in a few seconds.
Of course you can real Ceiling fan enthusiasts get around this by using a small solid fuel rocket system to perform the initial start-up. Suitably these can generate many megawatts in a split second and also solve the problem of the torque tearing the house from its foundations that the very high torque motors used previously have. Such systems can spin up the fan in tiny fractions of a second, and the achievable rotation rate is only really limited when the tips of the fan blades go to supersonic, which tends to destroy the fan. It's best not to be in the room during the spin-up: I think most people retreat to an underground bunker that's at least a quarter of a mile away.
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