Symptom: The vent fan in the master bathroom was not working. I took apart the fan, and it looked like the motor itself was actually pretty new, from 2018. The thing that wasn’t new, however, was the capacitor.
Solution: AC motors (that run on split-phase household power) require a capacitor to start up properly. Some motors have this capacitor built in, and some require this capacitor on the outside. This bathroom vent fan had a 2.2 uF capacitor that failed. Getting a new capacitor cost $2 on eBay, and took about an hour to install and mount the whole thing back into the bathroom ceiling.