What Is The Difference Between Motor With 1 Capacitor, 2 Capacitors And No Capacitors

Just a single speed. 1720 RPM.
I was spinning the shaft by hand clockwise and before it stopped spinning I plugged it in and it spun clockwise.
Spin shaft counter-clockwise and plug in before it stops and it spins that direction with no problem also.

A simplification

A single phase AC source will not create a rotating magnetic field. A single phase induction motor requires a method of causing it to rotate in the desired direction at start up it will then continue to operate in that direction until stopped. Hence the starting coils mentioned above, these are located out of phase and cause the armature to rotate in the biased direction during starting and are then often disconnected.

In a 3 phase AC source the phases are 120° apart and will always result in a rotating magnetic field.

DC will not generate a rotating magnetic field either, this is what the internal or external commutator does, it creates a rotating magnetic field mechanically or electronically.

A stepper motor is basically a permanent magnet DC motor with outside commutation.
 
Will I need to add a capacitor to this motor?
If so, what size and type?
A wiring diagram with a switch would be helpful too.
 
Will I need to add a capacitor to this motor?
If so, what size and type?
A wiring diagram with a switch would be helpful too.


We don't have enough information to answer these questions, but guessing it does not require a capacitor. Need to identify (using an ohm meter or opening the motor up) your start and run windings. This will determine how to wire it up to a drum switch.

By spinning your rotor by hand and plugging it in, you were providing the start winding function.
 
WreckWreck and CraigB1960 are both correct, we need a better pic of the motor body and connections to give an accurate answer. Off the top of my head, I would say you have a A/C Split phase motor with differential windings. If that's the case a pic of connections and motor frame will tell us everything we need to know.
 
Here is the complete motor. No mount, just 2 studs sticking out.
No way to get to any other wires without taking the motor apart.

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