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

84

MOMENTUM AXIS

axis. It is clear (Fig. 43) that it makes an angle y with GC
Af2 sin a
given by tan y = A
It will be seen that precession of the momentum axis necessitates a corresponding precession of the axle of the top, since
both lie in the azimuthal plane.
Hence we may discuss the motion of
the top by considering the rotation
H of the momentum axis (see Art. 85).
/ j In steady motion the momentum
'/ 4A \ axis coincides with the axis of re\ sultant angular momentum.
85. Torque required to rotate the
|,/ momentum axis. Referring to Fig.
I/ [ b A 20, p. 37, let OX, OY, OZ be any./ Ad g three mutually perpendicular lines,
-/ /, and let OX be the momentum axis
y/,/ / Aat any instant, and take OA to,'A sis2a represent the magnitude (M) of the.^c..... — -momentum.
'Let Q be the angular velocity of
FIG 43. OX round OZ (see Art. 40), so that
after time st, the angular momentum
is represented by OA', where the angle A OA'= t.
Then if A'B' be drawn parallel to AO, OB' represents the

L., ' M,/
#/

B

/
/!

/

Y
FIG. 44.
change of angular momentum in time dt, since OA and OB' are
equivalent to OA'.