The problem is that any engine is not 100% efficient – that is that not all the energy you put into the generator will come out as electricity. Some will become heat, some sound, etc. You have to put some energy into the alternator to make that work, which usually is some mechanical force like a turbine powered by steam. The way you have described it is actually less efficient than just having an electric motor or an alternator – you will get less electricity out of the alternator than you put into it with the motor. This is as I said because of energy loss in the system.
Again my answer was somehow deleted so apologies if you get this twice. Steven and Ed are right that you need something, fuel or so, to keep the system going. A long time ago, in the middle ages, people were trying to come up with a machine that would move, without additional energy, in perpetuity – that is why they called it the “perpetuum mobile”. However, no matter how hard you try, there will always be something to slow down the system (e.g. friction at the bearings) so that it simply can’t work.
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