Stewart 16.5 #37 (a)

Let

be a rigid body rotating about the

-axis. The rotation can be described by the vector

where

is the angular speed of

, that is, the tangential speed of any point

in

divided by the distance

from the axis of rotation. Let

be the position vector of

.

By considering the angle

in the figure, show that the velocity field of

is given by

.

I'll try to produce the figure mentioned in the problem if anybody wants it, but basically

is the measure of the angle between

and

.

Now part of my problem is that I know jack about physics so I don't really know what a velocity field should represent. Angular speed? Tangential speed? I'm not totally clear on what the difference between these are anyway. Seriously, I know nothing about physics, I haven't taken a single class in it.