Do rotary shutters have uneven exposure?

Question

While exploring shutter angles, I found out about the rotary shutter. I understand that these were developed primarily for movie cameras, but the first thing that came into my mind was: surely this mechanism would have created an uneven exposure?

Mathematically, as the radius of the circle increases, the diameter increases too, so that the part of the shutter further from the axis of the circle would be exposed for a longer time?

References:

• https://en.wikipedia.org/wiki/Focal-plane_shutter#Rotary_focal-plane_shutter
• https://www.red.com/red-101/shutter-angle-tutorial

In this crude example I've drawn, when turning clockwise, the black shutter exposes a top corner first:

but as it continues turning, the lower part is exposed fully for what appears to be a longer time:

...while the upper corners are not exposed:

So wouldn't the upper part of the sensor be less exposed? And if so, how was this compensated for?

Answer 1

No, because the farther from the center it is the greater the rotational velocity is. I.e. the shutter travel speed is proportional to the radius. If you continue your simulation, the bottom of the sensor will be covered before the top is.