I found a great video in which Alexander Fox helps us to understand the shutter in traditional film cameras, and how it relates to modern DSLR video.
Summary: To get a standard narrative film look, you want your shutter speed to be half your frame rate (or your shutter angle to be 180°).
Watch the video to find out why the standard film shutter angle is 180° and how that equates to half of your frame rate.
Shutter Angle = Frame Rate × 360 / Shutter Speed
example: 180 = 24 * 360 / 48
This can be spun around:
Shutter Speed = Frame Rate × ½
example: 1/48 = 1/24 * 1/2
Why We Care
Decreasing your shutter speed (increasing your shutter angle) without adjusting your frame-rate to match will increase motion blur in your footage.
Increasing your shutter speed (decreasing your shutter angle) without adjusting your frame-rate to match will decrease motion blur in your footage, but cause a staccato effect if you push it too far. This Saving Private Ryan Effect can help tell your story if used deliberately, but you'll want to avoid it otherwise.