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These are both AC motors. The one with exposed wiring is set up for 115v (110-120v is normal household voltage) and draws 5.3A to spin at 1645 rpm. The enclosed motor is set up for 220V, spins at 3450 rpm, and draws 2.3A.
Both of these are going to spin way too fast to direct drive your cupcakes and you'll need a hefty inverter to change the direct current from a car battery into the alternating current that these need. They may also be missing some capacitors needed to start or run them, but maybe not.
My suggestion (which you explicitly did not ask for) is to use a DC motor with a gearbox already installed. Maybe try to find some really light duty used winches. If the cupcakes are light enough you may be able to get away with power window motors from the scrap yard. If they're super light, windshield washer motors might work.
=Walter Stokes
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