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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** = ω**k**, 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

be the position vector of *P*.

Find **v**.

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Math

Calculus

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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