Hi Lianna. I guess you could use three separate pieces of film to overcome the problem that sdotkling points out, but that would raise its own problems such as having to position the three individual pieces of film into their little slots in the disk. I think he or she is right that the disk shape would require starting with a large piece of film (or a lot of fussy manufacturing of it). Unless modern construction technique (eg robotics) meant that cutting and placing the three pieces of film would be not a deal breaker.
There have been lots of rotary shutters. I am not an expert, just intrigured, but a little slit moving across the film plane will do the trick. Most modern shutters work that way, by the way, of a slit moving across the film or sensor. A lot of people think a shutter works by opening and shutting like an iris but most really do not work that way.
In some ways having the three negs placed in a circle around the shutter could be really effective if you can accept the cost of inserting the film. The strip of three negs would be a lot cheaper in that regard. However it has its own problems, you are going to have to design a light proof mechanism as the holder slides back and forth.