Solved: Curl and angular speed Consider the rotational

Chapter 14, Problem 52

(choose chapter or problem)

Curl and angular speed Consider the rotational velocity field v = a * r, where a is a nonzero constant vector and r = 8x, y, z9. Use the fact that an object moving in a circular path of radius R with speed _ v _ has an angular speed of v = _ v _ >R. a. Sketch a position vector a, which is the axis of rotation for the vector field, and a position vector r of a point P in _3. Let u be the angle between the two vectors. Show that the perpendicular distance from P to the axis of rotation is R = _ r _ sin u. b. Show that the speed of a particle in the velocity field is _ a * r _ and that the angular speed of the object is _ a _. c. Conclude that v = 12 _ _ * v _.