When you rip something, you tear it quickly or forcefully. It's almost always better to rip off a Band-Aid than to peel it off slowly.
You can rip a piece of paper in half, or rip a hole in the roof of your tent. When you tear, split, or pull something apart, you rip it. You can also rip figuratively — like when your move to a new city rips you apart from your best friend. A rip off is a bad deal or a swindle, a phrase that's been popular since about 1970, although rip meaning "steal" was used as prison slang much earlier.