Chapter 11, Problem 30P

(III) Show that the velocity $\stackrel{\to }{v}$ of any point in an object rotating with angular velocity $\stackrel{\to }{\omega }$ about a fixed axis can be written

$\stackrel{\to }{v}=\stackrel{\to }{\omega }\times \stackrel{\to }{r}$

where $\stackrel{\to }{r}$is the position vector of the point relative to an origin O located on the axis of rotation. Can O be anywhere on the rotation axis? Will $\stackrel{\to }{v}=\stackrel{\to }{\omega }\times \stackrel{\to }{r}$ if O is located at a point not on the axis of rotation?