I was spinning a cylindrical bottle of superglue, and a sphere formed in the middle until the bottle stopped again. Why is this?
The "sphere" you see is an illusion caused by "persistence" in your vision. If you take a long exposure with a camera you will see something very similar, but with a very fast exposure you will not see the sphere. A long exposure in effect averages a lot of "snapshots". The spherical region you see is the region that is always covered by the cylinder regardless of its angle while it is spinning. The blurred regions you see on each side of the spherical region are only covered part of the time, so you see the background in those regions part of the time. At each point, your vision averages what it sees over a short period of time that can range from a few hundredths of a second to several seconds. That's what makes movies work: individual frames are displayed, but quickly enough that you can't see the transition occur.