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

APPENDIX.
Explanation of the precession of a wheel from conservation
of angular momentum. If we have a particle P constrained to
revolve about a fixed axis OC, then, by the principle of
conservation of angular momentum, the nearer it gets to this
axis the faster it must revolve, and vice versd. (We may
imagine, for instance, the particle P, Fig. A, to be a heavy bead
sliding on a wire OA which is turning about 00.)
C
__- A
I A ---FIG. A.
This acceleration or retardation of rotation represents the
action of a single force * in the appropriate direction on the
particle P.
Thus, if the particle is getting nearer to the axis, its accelerated
rotation is caused by the action of a certain force in the
direction PQ of its rotation; while if the particle is moving
away from 00 this force acts in the direction PQ' opposing
its rotation.
Now let us apply this.
We may consider the rotating wheel to be composed of sets
of four particles, of which A, B, C, D (Fig. B) are a type,
situated symmetrically as shown in the figure, and rigidly
attached to one another and to the axle OX (perpendicular to
the plane of the paper) about which they are rotating in a
direction shown by the arrow-heads.
* There will really be a number of forces acting on the particle P due to the
action of the various constraints by which it is attached to the frame. The
above force is a single force equivalent to this set of forces.