### Angular Velocity Vector

When working with rotations, it is convenient to define the*angular-velocity vector*as a vector pointing along the

*axis of rotation*. There are two directions we could choose from, so we pick the one corresponding to the

*right-hand rule*,

*i.e.*, when the fingers of the right hand curl in the direction of the rotation, the thumb points in the direction of the angular velocity vector.

^{B.18}The

*length*should obviously equal the angular velocity . It is convenient also to work with a unit-length variant .

As introduced in Eq.(B.8) above, the mass moment of inertia is given by where is the distance from the (instantaneous) axis of rotation to the mass located at . In terms of the angular-velocity vector , we can write this as (see Fig.B.6)

where

*vector cross product*(defined in the next section), we will show (in §B.4.17) that can be written more succinctly as

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Vector Cross Product

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Two Masses Connected by a Rod