I need a word for the act of impotently whining and crying over something that you can't change —like, for example, moaning and groaning about what to do now that Trump is President-Elect instead of finding something actually useful to do.
"Hand-wringing" is used to express the idea that someone is "fretting" over something and instead of taking positive action, just stands by, impotently wringing their hands.
Hand-wringing as defined by MWO:
an overwrought expression of concern or guilt
This expression dates back to 1922 (per MWO).
I think the word moping works.
To be unhappy and unwilling to think or act in a positive way, especially because of a disappointment.
'There's no point in sitting at home and moping - get out there and find yourself another job!' (Cambridge Dictionary)
‘But he frequently has been his own worst enemy by moping and overanalyzing, leading to a loss of confidence and bad habits.’ (OED)