If #\vec{F_{}}# is the force generating the torque #\vec{\tau_{}}# on the gyroscope, the precession frequency #\omega_p# is related to the angular momentum #\vec{L_{}}# as follows. The angular momentum itself is related to the moment-of-inertia #I# and spin frequency #\omega#.

**Torque** : #\vec{\tau_{}} \equiv \vec{r_{}}\times\vec{F_{}}=\frac{d\vec{L_{}}}{dt}#,

**Angular Momentum**: #\vec{L_{}}\equiv I\omega#

**Precission Frequency**: #\omega_p = 1/L\frac{dL}{dt}=\tau/L#

The torque generating force is the weight ( #F=Mg#) of the spinning disk which acts vertically down. Since the gyroscope's axle is horizontal to the ground, #\vec{r_{}}# and #\vec{F_{}}# are perpendicular to each other.

#\tau = r.F.sin90^o=r.Mg.sin90^o=Mgr#

Moment of inertia of a disk of mass #M# and radius #R# is #I=\frac{MR^2}{2}#

Angular momentum #L=I.\omega=1/2 MR^2\omega#

Precessional frequency #\omega_p = \tau/L = \frac{Mgr}{1/2MR^2\omega}=\frac{2gr}{\omegaR^2}#

**Given** : #R=49cm=0.49m#;#\quad##r=4cm=0.04m##\quad##g=9.8ms^{-2}#

#\omega=990 # rev/min #=33\pi # rad/s,

#\omega_p = \frac{2gr}{\omegaR^2}=0.03148 # rad/s #=0.3007# rev/min.