How fast is this planet spinning?

If one stood right next to the North Pole it would take a day for the earth to rotate you right round. If you stood at a point on the equator it would also take a day for the earth to rotate you right round. So is time travelling faster at the equator?

mirror ball

If one were to create a sphere, say 8-10 metres in diameter, the interior surface of which was mirrored and then imagine it was bright inside so that one could see clearly. If you were then to be placed at the centre of that sphere with your reflections all around you, what would those reflections look like?

snippet

Picasso regarded the shattered mirror. Looked at the myriad faces gazing back at him. Each viewing him from their own particular perspective and unique reality. All those eyes seeing a distinct and different him; the one observer in this scene. The origin of their existence and the single subject of their dispassionate gaze.