What Is Shutter Angle?
The "shutter angle" is a useful way of describing the shutter speed relative to the frame rate. The term is a relic of rotary shutters in film-based movie cameras, where a disc with an angled opening would spin and let in light once per revolution to expose each frame. The larger the angle, the slower the shutter speed—all the way up to the limit of 360 degrees, where the shutter speed could become as slow as the frame rate. At the other extreme, the shutter speed can be made arbitrarily fast by decreasing the angle.
Although current digital motion-picture cameras (including HD video DSLRs) don’t necessarily control shutter speed in this way, the shutter angle terminology has persisted as a simple and universal way of describing the appearance of motion blur in video. If one wants subjects that are blurred for a greater fraction of their frame to frame displacement, then one would choose a larger shutter angle, and vice versa.
Controlling The Appearance In Your Footage
By far the most common setting for cinema has been a shutter angle near 180 degrees, which equates to a shutter speed near 1/48 of a second at 24 fps. Any larger, and motion appears more smeared or "video-like" since the end of blur in one frame extends closer to the start of blur in the next frame. Any smaller, and the motion appears more stuttered and disjointed since the blur gap increases, causing frames to become more like discrete images.
Although the above example is helpful for understanding the underlying behavior, one typically doesn’t see motion blur within each frame as one would in a still image. In practice, the shutter angle also has a more subjective influence on the overall feel of motion footage—even if one isn’t necessarily aware of the precise settings.