Aw dang is the word that you say when you are slightly disappointed
, but you don't care much about it.
If you are very disappointed, you will not use this word.
Also, if you, for example, don't make a part you really hoped for, you would most likely not use this word. However, if your friend doesn't make the part in a play they wanted, it would make sense to say aw dang. This said, you could also use this word when you are truly sad, but don't want anyone to know (see example two).
This word is closely related to the word oh dang