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)
denotes the orthogonal projection of
![]() |
Using the vector cross product (defined in the next section),
we will show (in §B.4.17) that
can be written more succinctly as