Past exam of the mathematical methods II course of the University of Oxford / 2014 resit / 11 / a / Solution

Write $\mathbf{\omega }=({\omega }_x,{\omega }_y,{\omega }_z)$. The cross product gives $\mathbf{v}=({\omega }_{y}z-{\omega }_{z}y,{\omega }_{z}x-{\omega }_{x}z,{\omega }_{x}y-{\omega }_{y}x)$. Since the components of $\mathbf{\omega }$ are constant, direct partial differentiation givesThusThe vorticity is twice the local angular velocity of this rigid-body rotation.