The "norm" for video is to shoot with the shutter open for half the duration of each frame. That means 1/120 if you're shooting 60 fps. 1/100 if you're shooting 50 fps. 1/60 if you're shooting 30 fps. 1/48 (or 1/50 if that's all that's available) if you're shooting 24 fps etc.. This is alternatively known as 180 degrees, as it dates back to rotary shutters on film cameras and projectors. A faster shutter speed is possible but with movement you will get a stuttery effect, a bit like a cartoon flipbook, because less motion-blur is captured. Having said that I've published loads of video with a faster shutter than 180 degrees. With a static shot it doesn't matter. I've even used 360 degrees (1/30 at 30p) in dark situations, rather than increase the ISO. Fast shutter speeds can be good for doing slow motion in post-production, where the motion interpolators like sharp frames to work with.
Not sure how strobe sync is relevant to video.