91Ó°ÊÓ

For any moving body the ratio of the angular momentum with the angular velocity is known as the moment of inertia.

The precession angular speed is related to the gravity by the following formula,

$\mathrm{Î\copyright }=\frac{mgr}{I\mathrm{Ó\neg }},withw=mg$

Here, $\mathrm{Î\copyright }$is precession angular speed, $m$is the mass of the object, $g$is the acceleration on the object, $r$is the radius, $I$is the moment of inertia, $w$is the weight of object, $\mathrm{Ó\neg }$is the angular velocity of the object respectively.

Acceleration due to gravity on moon $g_M=0.165g$,

Acceleration due to gravity on earth is $g$.

Precession on earth, ${\mathrm{Î\copyright }}_M=0.50rad/s$

For the gyroscope$m,r,I,and\mathrm{Ó\neg }$are the same on the earth and moon, so from the formula,

localid="1667991353871" $\frac{\mathrm{Î\copyright }}{\mathrm{g}}=\frac{\mathrm{mr}}{\mathrm{IÓ\neg }}=\mathrm{constant}$

So, if you will take the precession of earth and moon that will show the following relation, on putting the values in the relation we will find the required precession rate on the moon,

localid="1664030062874" ${\mathrm{Î\copyright }}_M=\left(\frac{g_M}{g_E}\right){\mathrm{Î\copyright }}_E$

localid="1667991386314" $$\begin{gathered} =\left(\frac{0.165\mathrm{g}}{\mathrm{g}}\right)\left(0.50\mathrm{rad}/\mathrm{s}\right) \\ =0.0825\mathrm{rad}/\mathrm{s} \end{gathered}$$

Hence, the precession rate on moon will be localid="1667991407975" $0.0825\mathrm{rad}/\mathrm{s}$.