I want to shoot a video for my iPhone app demo. My idea is shoot a phone running the app, and the iPhone is relatively still in the video, while I could move the camera around, so the background changes, but not the phone. Is there something available to do this? I would imagine something like an extension arm, one side holds the camera, and the other side holds my phone. I don't know if this thing exists nor not. Please help, thanks! (What I have now is a DSLR and a tripod)
Yes, what you are talking about falls in the realm of rigging. There are lots and lots of rigging products available, but most of the specialty built rigs are going to be very expensive for your needs (hundreds to probably over a thousand USD). If you aren't turned off by the price, I suggest looking at rigs in a web store like B&H to find something that will suit your needs and allow attaching an extension and the phone mount.
You might be better off to do something yourself to save money. You should be able to buy a basic mount plate that you could bolt to a pipe and then on the other end attach a device holder for the phone. I'd probably try and do it with something like a Trident case that will look like a nice case on the phone while allowing you to attach the mount to the back of the case securely. It will still probably run you a couple hundred USD though, even making it yourself. (Trident cases and the stand for it alone will run you $70 or so.)