Velocity of rotation of a sphere

Assuming that we have a sphere of ~$$6000$$ meters in diameter, which is rotating about an axis with an equatorial velocity of $$v = 250$$ meters per hour, how can I determine the velocity of this rotation at an other point other the equator?

The time required for one full round trip is the same everywhere: $$2\pi r/v$$. What you need to know is the distance traveled: it is obviously $$2\pi r$$ at the equator and $$0$$ at the pole.
At a general latitude $$\phi$$, trigonometry will tell you that the distance is $$2\pi r \cos(\phi)$$, so the speed is $$\frac{2\pi r \cos(\phi)}{2\pi r/v}=\cos(\phi) v$$
At a latitude of $$\alpha$$, you uwill have a velocity of $$v\cos\alpha$$.
Then, the rotational speed is proportional to radius, meaning that $$v=v_0\cos(\theta)$$.