The standard calculation is:
[frame rate] * [shutter angle] = Shutter
Consider an example from film: 1/24 fps * 180/360 = 1/48 shutter.
Beyond that calculation, experimentation is your friend.
Trying to run through the various calculations gets cumbersome. For example, 1/24 * 1/x = 1/2000
1/[24x=2000]
x=83.3
1/83.3=y/360
y=4.3 degree shutter
Feel free to check my math.
IMO, you should keep the shutter mostly fixed unless you’re doing specific effects (Saving Private Ryan, for example with a narrow shutter). But if the whole movie is that way, then nothing is that way. Make sense?
Video is 1/29.97*1/2=1/60, so that’s where a quote-en’-quote “normal” picture should be.