A vortex that rotates at constant angular velocity about


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.

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Mathematics: A vortex that rotates at constant angular velocity about
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