If a sphere was rotating about it’s axis at relativistic speeds what would happen from the perspective of an observer looking at the sphere with the axis of rotation parallel to them (directly up and down). What would happen from the prospective of an observer looking straight down on the sphere (such that the axis appeared to be a point)?

I believe that, nothing would appear to happen to the sphere, although there would be a change in objects that may or may not be on the surface of the sphere.

What exactly do you mean. Wouldn’t the outer part of the sphere be the fastest moving and therefore most relativistic part of it? What if it was a hallow sphere?

It's more complicated than it first seems IMO as it's spinning it must be rotating and not inertial so we'd need GR I suspect...

It's more complicated than it first seems IMO as it's spinning it must be rotating and not inertial so we'd need GR I suspect...

 

Not quite, see my post on energy independent of spacetime.

The sphere itself is stationary, relative to you. Although the very outside of the sphere would be moving the fastest and in this case the speed of light, so I believe that you would only see time or length contraction on the outermost surface of the sphere (from your perspective).