The motor is a A.O Smith Century 56-Frame Two-Speed motor. It runs on 240V single-phase. Here’s the only reference I found (PDF), search for B2235.
If such a motor would be hooked to a 120V circuit, would it develop enough torque to start? Would the rotational speed be the same? I
am also interested about the effect on capacitor(s) and centrifugal switch.
Edit: Edited to just put emphasis on the theorical aspects because I had a feeling the answers would tend toward how to actually get 240V to the motor.
Testing the motor on your workbench at 120 volts should be as safe as your test setup. Ground the motor frame. Fasten it down so it doesn’t roll off the bench when it starts. Be ready to switch it off if something goes wrong. The motor should produce about 1/4 of rated torque with 1/2 of rated voltage. If the bearings are ok and the switch is ok, it should accelerate to near rated speed and activate the centrifugal switch. Be ready to shut it off if the switch doesn’t activate right away. You should monitor the current with an ammeter and be ready to shut the motor off if it doesn’t drop to a low value quickly when starting. The starting inrush will be something like six times rated current.
If that all goes ok, you should monitor the current and be ready to shut it off the first time you try it at 240 volts.