Tangential Velocity as a Cross Product
Referring again to Fig.B.4, we can write the
tangential velocity vector
as a vector cross product of
the angular-velocity vector
(§B.4.11) and the position
vector
:
To see this, let's first check its direction and then its magnitude. By the right-hand rule,
![$ \underline{\omega}$](http://www.dsprelated.com/josimages_new/pasp/img2799.png)
![$ \underline{x}$](http://www.dsprelated.com/josimages_new/pasp/img260.png)
![$ \underline{v}$](http://www.dsprelated.com/josimages_new/pasp/img2686.png)
![$ \underline{\omega}$](http://www.dsprelated.com/josimages_new/pasp/img2799.png)
![$ \underline{x}$](http://www.dsprelated.com/josimages_new/pasp/img260.png)
![$ \pi /2$](http://www.dsprelated.com/josimages_new/pasp/img82.png)
![$ \,$](http://www.dsprelated.com/josimages_new/pasp/img196.png)
![$\displaystyle \left\Vert\,\underline{\omega}\times \underline{x}\,\right\Vert \...
...,\right\Vert\cdot\left\Vert\,\underline{x}\,\right\Vert \eqsp \omega R \eqsp v
$](http://www.dsprelated.com/josimages_new/pasp/img2849.png)
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Mass Moment of Inertia as a Cross Product