What would happen if the Earth rotated like this, with the poles and equator moving at different rates?
The Earth's crust is solid, so everywhere rotates at the same rate.
Check out The Earth & Beyond section to find out more about the rotating Earth.
Here is another amazing picture showing the speed of rotation of material in the Sun. It was made using observations from SOHO. The colours represent speed; red material is rotating the fastest, dark blue is rotating the slowest.
This happens because the Sun is not a solid but is made of plasma.