I'm trying to learn about this motor and to learn it I need to read about it and to read about it I first have to figure out which kind of motor is it.

I think it's a capacitor start and run small ac motor but I'm not very sure.

 

A cap start / run motor, would have a centrifugal switch, and a centrifuge on the rotor...
This appears the stator out of a ceiling fan, or a small HVAC fan-type motor...

A capacitor in circuit would control direction of rotation, based on wiring scheme.

Best guess - the picture shows a pen for size... is it out of a bathroom vent ?

 

A cap start / run motor, would have a centrifugal switch, and a centrifuge on the rotor...
This appears the stator out of a ceiling fan, or a small HVAC fan-type motor...

A capacitor in circuit would control direction of rotation, based on wiring scheme.

Best guess - the picture shows a pen for size... is it out of a bathroom vent ?

Nah, I'm sure it's not a ceiling fan motor. Maybe this motor is from an evaporative cooler. But I am not able to figure out where is its' so called bearing cause I've heard that "bearing" word with evaporative cooler motor.

 

I think it's a capacitor start and run small ac motor but I'm not very sure.

It appears to be a 1ph cap start/run induction motor (no centrifugal sw), the fact there is two conductor colours instead of three sort of rules out a 3ph induction motor.
The motor appears on the smaller size going by the pen in the pic, also indication start switch not usually required.
Just combined start/run capacitor.
There also looks to what could be a timing belt style pulley used?
Max.

 

Looks to be a squirrel cage induction motor.

 

Looks like an old oscillating fan motor or a ceiling fan motor to me.
I don't see a run cap, but it does have a thermal fuse.

Are there any markings on the casing?
The bushings are in either end of the casing.

What are you wanting to do with it?
One of the windings is broken, but might be repairable.
The thermal fuse would be inside the insulated section.
That can easily be checked for continuity.
Just remove the insulation and check it with a meter, from both ends.
If the meter beeps, the fuse is good.
If not, the fuse is bad and must be replaced.
Looks old, but not too old.
Probably 1970's I'ed guess.
(not 1930's 40's, etc.)
A better picture of the armature might reveal some things as well, as to it's repairability.
Are the shafts worn out, etc.?