A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field v=w(-yi+xj). a. Sketch, on a separate sheet of paper, the vector field with w=1 and the vector field with w=-1. Then determine the speed Vert{vâ}Vert of the vortex as a function of the distance from its center, r.
b. Compute div vâ and curl vâ.
c. Compute the circulation of vâ counterclockwise about the circle of radius R in the xy-plane, centered at the origin.