That's called a Starter Cap, IIRC..
I think it would take a lot of work to convert a washer motor into a generator.
I once salvaged a washer motor. I looked at the wiring diagram and found it had two speeds.
I used it to power a dual-speed drill press for about 10 years. Very useful and reliable motor. People use washer motors to power all sorts of shop tools.
When I replaced my DIY drill press with a Chinese drill-mill, I dumped the old one
on the curb and it was gone within minutes.
But, when I looked at my new drill-mill, the motor looked identical! (My Chinese band saw has the same motor too)!
There seems to be a lot of people using DC generators on bikes..
Low-tech Magazine: Bike powered electricity generators are not sustainable
If your motor is like this one,
Induction Motor How it works - YouTube
Then you would need to remove the rotor and replace it with a spinning PM..
Seems like a lot of work to me..