^
Normally I just take things like that on a "that's just the way things are" basis without doing the calculations.
And I don't actually don't want to do the numeration now, but somebody can attack it if they want.
But remember that with a certain frame (or camera scan) rate, AND a certain RPM, what appears to be a single one of the seven cylinders is not actually the same cylinder in each frame.
Similarly, nor is it necessarily the same prop blade.
Figuring, with numbers plucked out of the air*, a 1000 RPM rotation rate, AND a 1000 per second frame rate, everything would seem to be standing still.
The same would be true, just looking at the prop, if the frame rate were 500 per second, but in each frame, it would be a different (though identical) prop blade, so it would still look as if the prop were standing still.
Similarly, the cylinders would seem to be standing still, but it may be a different, though visually identical, one of the seven cylinders in each frame.
But the frame rate always stays the same in the camera as we change the RPM from, say, 500 RPM to 1000 RPM, so the camera would be capturing each of the identical successive cylinders in a different relative position with each frame, making it look as if it were advancing at some RPM and going backwards at another RPM. This advancing and retarding, with each cylinder being 51.42° away from the next cylinder in line, may or may not coincide with the advancing and retarding of the prop blades, which are 180° apart.
In our imaginary situation, at, say, 750 RPM it may look as if there were four prop blades.
So, at varying RPMs but a constant frame rate, the cylinders may seem to be standing still while the prop looks like it is slowly rotating, or one may look like it's turning one way while the other is rotating oppositely.
The thing to keep in mind is that while either the prop blades or the cylinders may appear to be standing still in each frame of the camera, they may or may not actually be the very same prop blade, OR the same cylinder in each successive frame.
The simple math involved is left to the simple student.
Corrections and comments invited.
Terry, 230RN
* "plucked out of the air" is frequently abbreviated in high level scientific discussions as a "PFA" or "plucked from the air" number.
The PFA frame rate and RPM both being 1000 were PFA-chosen to make the concepts somewhat simpler.
<Edited for minor grammar corrections.>