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
terms of the angular-velocity vector
, we can write this as
Vector Cross Product
Two Masses Connected by a Rod