Question: A vortex that rotates at constant angular velocity ω about the z-axis has velocity vector field v→ = ω(-yi→ + xj→).
(a) Sketch the vector field with ω = 1 and the vector field with ω = -1.
(b) Determine the speed v→ of the vortex as a function of the distance from its center.
(c) Compute div v→ and curl v→.
(d) Compute the circulation of v→ counterclockwise about the circle of radius R in the xy-plane, centered at the origin.