An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.

CHAPTER II.

REPRESENTATION OF ANGULAR VELOCITY.
PRECESSION.
20. If a body have a point fixed, then the angular velocity or
rotation of the body has three essential properties. For:
(1) It is about a definite axis.
(2) It is in a definite direction about that axis.
(3) It is of definite magnitude.
These three properties can be represented geometrically, for:
(1) Through a fixed point, 0 say (to represent the fixed
point in the body), can be drawn a straight line OA to
represent the axis of rotation.
(2) The direction of rotation about this axis can be represented by considering as positive the rotation of a
A' 'o A
FIG. 14.
left-handed screw as one looks along the axis. For
instance, in the adjoining figure the same rotation is
+wo about OA or A'A or -e about OA' or AA'.
(3) Finally, we can mark off the length OA to represent
on any scale we like, the rmagnitude of the rotation.
Hence it follows that angular velocity, like linear velocity, is
a vector quantity.
21. On the physical meaning of composition of velocities.
Relative and total velocity. When we say that a particle P
simultaneously possesses two velocities u and v in two directions,
OA, OB inclined to one another at an angle a, we do not mean
that it is moving in space in two directions at once. That is
impossible, for it moves with a definite velocity in a definite
direction in space. The physical meaning of the "two simultaneous velocities" will be best understood by supposing (Fig. 15)