Originally Posted by

**ragnar** Stewart 16.5 #37 (a)

Let $\displaystyle B$ be a rigid body rotating about the $\displaystyle z$-axis. The rotation can be described by the vector $\displaystyle {\bf w} = \omega {\bf k}$ where $\displaystyle \omega$ is the angular speed of $\displaystyle B$, that is, the tangential speed of any point $\displaystyle P$ in $\displaystyle B$ divided by the distance $\displaystyle d$ from the axis of rotation. Let $\displaystyle {\bf r} = < \! x, y, z \! >$ be the position vector of $\displaystyle P$.

By considering the angle $\displaystyle \theta$ in the figure, show that the velocity field of $\displaystyle B$ is given by $\displaystyle {\bf v} = {\bf w} \times {\bf r}$.

I'll try to produce the figure mentioned in the problem if anybody wants it, but basically $\displaystyle \theta$ is the measure of the angle between $\displaystyle {\bf r}$ and $\displaystyle {\bf k}$.

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.