The widely accepted rule of thumb for shooting timelapses is that your shutter speed should be 1/2 your interval. What this means is if you are shooting one shot every 3 seconds, then your ideal exposure is 1.5 seconds.
The point of shooting timelapses is to end up with video at some point, right? Film cameras have dealt with this issue for some time now. In a film camera, a piece of film rapidly advances one frame, stops, is exposed to light, then the exposure stops, the film advances and the whole process begins anew. This process can occur 12, 24, 30 or more times per second. The camera needs some time to move the film into position, so it spends some time with the shutter closed (moving film) and then it spends some time with the shutter open (exposing film) The standard for a long time now has been to spend half of the time exposing, and half of the time moving film (not exposing.) On film cameras the shutter is often on a shaft and rotates through the film plane. Thus a 180 degree shutter literally is a half circle that blocks the film from getting light half of the time.
Well, that’s still a good question. Digital cameras can go from practically 0 degrees up to literally 360 degrees. The big difference is in what it looks like. Motion blur is what this is really all about. Regardless of your exposure or frame rate, a shorter exposure will have less motion blur on it. On the flip side of the coin, a longer exposure will have less action occur when the lens is ‘closed’ and it will look less strobe-like. The balance between those two things is how people decided on a 180 degree shutter, and that brings us back to shooting stills.
When shooting a timelapse, if your shutter speed is smaller than half of your interval then your video will start to look strobey. What I mean by that is that there is a continuity gap from one frame to the other. If the video is of a car driving, then the distance that the car moves between frames will increase and the resulting video will look jumpy.
If your shutter speed is larger than half of your interval you will end up with more motion blur. Trails will occur behind moving objects. This is generally less of a concern because our minds are much less confused by trails than by strobing. Strobing can be dissociative, while motion blur is more like an artistic statement.
In conclusion: Like all rules, this rule of thumb is meant to be broken but it can never be ignored.
Addendum: When you are shooting video in movie mode, this should also guide your shutter choices. If you shoot 720p 60, then you should have a shutter speed of 1/125, and if your are shooting 24fps, then it should be 1/50. Feel free to deviate but know what will happen if you do.