i have one of those motors out of my normal vacuum, not even a shop vac. it does indeed make 2hp. i'm going to use it on my kart but theres a couple problems.
1. AC/DC - household power is AC. this is what the motor is built for. Batteries supply DC power. Luckily for you, all vac motors are universal aka they run on ac and dc.
2. Voltage - wall power is 120 volt or thereabouts. a car battery is 12volts. you can run your motor on 12 volt without damage, but it will make 1/10 of the power. you can use a step-up transformer to turn 12v into 120v, but they are hard to find as the 12 volt side of the transformer will have 120 amps of current.
(volts x amps = watts, 120v x 12a =1440w, 12v x 120a = 1440w)
you can also use an inverter, which is basically a transformer that also converts dc to ac. your motor will be slightly more efficient running on the ac supplied by the inverter instead of the dc from the transformer
3. Driveshaft - First, the driveshaft is attached to a fan, to suck air in the vacuum. this is contained inside a housing usually making up half of the unit's volume. you will have to get this housing off, which isnt too hard. the fans inside should just come off easily after that. the exposed driveshaft is about a quarter inch diameter and 2-3 inches long on mine. it has no keyway, but does have threads on the tip. this connection at the driveshaft shouldnt be too hard to weld to your sprocket somehow
as a sidenote, the threads on the tip of the driveshaft perfectly fit the threads on the inside of the driveshaft in the bottom bracket of my bike (remove the nuts holding the pedals on, they shouldnt fall off.) this might help anyone wanting to convert a bike.