1. An unforeseen obstacle; SYN. hitch, rub, snag.
2. (Informal) An emotional preoccupation.

1. To interrupt a telephone conversation.
2. To put a telephone receiver back in its cradle.
3. To place on a hook or hanger designed for the purpose
4. To replace (a telephone receiver) on the cradle so that the connection is broken
5. To keep delayed, suspended, or held up
6. To cause to stick or snag immovably

When you hang something in a high place so that it cannot touch the ground, you hang it up.