How to calculate angular velocity about a second axis?

A point in space at $$(a,b)$$ revolves around the origin with an angular velocity omega. I wish to compute its angular velocity about a second axis, running parallel to the $$z$$ axis at point $$(x,y)$$. Obviously, this depends on the position (a,b) such that at point (a',b'), its angular velocity will be different than at point (a,b). Since the position depends on time, there should be a way to compute the angular velocity about axis (x,y) as a function of time. What is it?

• Angular velocity is usually defined for rotation around an axis (not point). Could you rephrase your question accordingly? – user1583209 Dec 11 '16 at 18:28

When you say angular velocity about a point you mean to say angular velocity about an axis. The equation is simple: $\omega =\frac{\vec{r} \times\vec{v} }{|r^2|}$ where $\vec{r}$ is the position vector from the axis(through a point) that you choose and $\vec{v}$ is velocity vector.
• If it's particle's orbit is circular, then the equation becomes simpler: $\omega = \frac{v}{r}$ – N. Steinle Sep 28 '18 at 3:12