Perhaps, having solved a very similar problem using an actual video camera on an actual spinning disk, I took the problem too literally. But I will not let this dissuade me from offering my critique of your answers. :)
Video cameras do not record a continuous stream of motion; instead they merely take many still pictures one right after the other. For either of your answers to work, the revolutions per second of the disk must be significantly less than the frames per second of the video camera. For example, with the two-camera solution, how can you tell whether the the disk spun 1 degree clockwise or 364 degrees counterclockwise in the frame interval before the color change?
For the one-camera solution, there is the additional problem that the rate of spin of the disk must be constant. But I suppose we can assume that from the wording.
As far as I know, the problem as it's worded cannot be solved no matter how many cameras you throw at it.