Question

This exercise demonstrates a connection between the curl vector and rotations. Let B be a rigid body rotating about the z-axis. The rotation can be described by the vector w = ωk, where ω is the angular speed of B, that is, the tangential speed of any point P in B divided by the distance d from the axis of rotation. Let 

r = x, y, z

 be the position vector of P.

Find v.

ZA
B
хк
(a) By considering the angle 0 in the figure, find the velocity field of B.
v = curl
w × r
v = w x div r
v = w X r
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Transcribed Image Text

ZA B хк (a) By considering the angle 0 in the figure, find the velocity field of B. v = curl w × r v = w x div r v = w X r