Does anyone know what application to open webcam.rar with?

RAR is an archive, like ZIP.

So try 7-Zip.

Wikipedia

Problem solved.

Problem is indeed solved, however, sometimes one decompression program does not work where another one does. To that end I shall mention Winzip, and also WinRAR. Winzip is a preference of mine based upon how easy or how flexible it is in terms of operation and general appearance on the screen. By example, there have been instances where 7zip or WinRAR simply haven’t been able to successfully open a rar file, but Winzip has.
That said, it’s not entirely advisable to have too many of these programs installed because it will end up bunging a lot of extras on the right-click context menu.