Hi, off the top of my head I can think only of the case you're actually mentioning, that is a change of state. You can "get strong by going to the gym" or you can "become" strong as well, both are equal there. You get old or you become old. Notice though that in the cotinuous form you tend to "get" rather than become. "I'm getting older and can no longer play football as I used to" "I'm becoming" doesnt sound right.
Bear in mind also "become" is always more formal. When it comes to emotions though, as you said "become angry", although correct sounds extremely awkward in colloquial contexts. You get angry, you get mad, you get upset, you get sad, you get excited.