Ouch
anger
angina
angst
anguish
anxious
hangnail
Maybe you're thinking, "What could 'hangnail' have to do with those other words?" As you may or may not know, the "hang" part of "hangnail" ("a small partly detached piece of dead skin at the side of the fingernail") has nothing to do with hanging, although it was clearly influenced by that word (think "hanging chad"): it's actually from Old English "ang", "painful".
And that is why I was wondering about such words as "angina", which causes chest pain, and "anguish", which is the result of pain. You'd think that, because of their semantic similarities, they'd all be one big thicket of interrelated etymology, wouldn't you?
And they are. The "ang" in "hangnail" (also "angnail" and "agnail", because "-ngn-" is not that easy to pronounce) is clearly descended from the Latin "angere", "to torment", which also gives us "anxious" and "anguish". These are all in turn descendants of the Indo-European "angh-", "tight; painful", which also gave us the Greek "ankhone", "strangling", from which we get "angina", with its suffocating chest pain. "Anger" is from Old Norse "angr", "sorrow", which also naturally enough descends from "angh-". And finally we have German "angst" (which in that language means simply "fear" but in English denotes a collision of apprehension, fear, depression, and nervousness): it too is descended, predictably enough, from "angh-".