Need help with this cal-4 question 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 ||ü|| of the vortex as a functionof the distance from its center, r.speed =(b) Compute div v and curl i.div v =curl v =(c) Compute the circulation of v counterclockwise about the circle of radius R in the xy-plane, centered at the origin.circulation =

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Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Vectors In Two And Three Dimensions

Section9.FOM: Focus On Modeling: Vectors Fields

Problem 12P

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Need help with this cal-4 question

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 ||ü|| of the vortex as a function
of the distance from its center, r.
speed =
(b) Compute div v and curl i.
div v =
curl v =
(c) Compute the circulation of v counterclockwise about the circle of radius R in the xy-plane, centered at the origin.
circulation =

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