Surface speed of a point, with a rotational axis and angular force

Question

I am implementing a plate tectonics simulation based on a paper. Most of it is quite easy to understand, but I get stuck on the following formula: $$s(\mathbf{p}) = \omega \mathbf{w} \times \mathbf{p}$$ With this formula, I can calculate the surface speed ($s(\mathbf{p})$) of a point ($\mathbf{p}$) by multiplying the angular velocity ($\omega$) with a normalised rotation axis ($\mathbf{w}$) and applying the cross product with the point. It might be important to note that the point is part of a rigid body because it is part of a plate. The thing I do not understand is what kind of value the angular velocity and normalised rotation axis. Could someone explain to me if both are a vector or only the normalised rotation matrix, and what kind of values the angular velocity and rotation axis can be? For example, giving an example with numeric values would be really helpful.

Answer 1

It seems to me that $\omega$ is a scalar value, and $\mathbf{w}$ is a vector of length $1$. You are probably used to having angular velocity as a vector:$$\vec\omega=\omega\mathbf{w}$$ As for numerical values, you can get them from the table 3. If $\mathbf{w}$ is perpendicular to $\mathbf{p}$, then $$\omega=\frac{|s(\mathbf{p})|}{|\mathbf{p}|}=\frac{v_0}{R}=\frac{100\mathrm{\ mm/y}}{6370\ \mathrm{km}}$$