I think your proposed design is flawed. If the intent is to capture a picture when there is movement in the room, the most sensible, simple and reliable solution is to run software on the PC to do motion detection. This software is freely available.
Although it's possible to use a PIR sensor as a trigger, it would be much more complicated (and so take more development, and be less reliable) and would give you zero advantage over the motion detection approach. It would also have some disadvantages, because the PIR sensor will be able to trigger on things outside the camera's field of view and under light conditions where the camera cannot operate, which will result in pointless triggering of the camera.
All that being said, if you want to take a picture when the PIR sensor triggers then you need to interface the PIR sensor to an Arduino (I haven't done that myself, but others have) and then have your sketch send a message to the PC when it is triggered, and have an application on the PC receive that message and trigger some 3rd party application to grab a webcam snapshot - again, the software to do that on the PC is freely available.