Velocity of rotation of a sphere

Question

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?

Answer 1

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 $$\frac{2\pi r \cos(\phi)}{2\pi r/v}=\cos(\phi) v$$

Answer 2

At a latitude of $\alpha$, you uwill have a velocity of $v\cos\alpha$.

Answer 3

The angular velocity is the same at all latitudes.

Then, the rotational speed is proportional to radius, meaning that $v=v_0\cos(\theta)$.