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, points up out of the page in Fig.B.4. Crossing that with , again by the right-hand rule, produces a tangential velocity vector pointing as shown in the figure. So, the direction is correct. Now, the magnitude: Since and are mutually orthogonal, the angle between them is , so that, by Eq. (B.16),

as desired.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University