To add to what CanadianDude said:
When you fly straight, things change in small ways from frame to frame. When you turn, the changes can be larger from frame to frame.
A higher frame-rate helps this because you're adding more frames per second of the same turn. This reduces the changes from frame to frame. If you go from 30FPS to 60FPS, you're capturing twice the frames, so each frame changes less from the previous frame.
If you can't (or don't want to) go to a higher frame rate, then you can slow the shutter down to give you image blur between frames. This makes it look more choppy because the brain sees the blur and movement from frame to frame and sees that as more natural, closer to the way we see (or think we see) movement in real life (since our eyes/brain don't see life as a series of sharp, static shots).
And in fact, that last thing is what people seek to do, because it mimics the look and feel of film (old film in a projector going at slow speed, such as 24fps). Use "the 180° Shutter Rule", where you set your shutter speed should be set to twice the frame rate (1/FPS x 2). With a frame rate of 24 FPS, set the shutter to 1/48 shutter speed (or close to it). Or 30FPS with 1/60 shutter speed
1/60 sounds fast, since we can take hand-held shots (without a tripod) with a normal camera and get a good shot, but it's only going to be sharp if people/things aren't moving much.
Hope that helps.
Chris
