91Ó°ÊÓ

$\begin{array}{l}\mathrm{R}=50\text{cm}\\ \mathrm{L}=11\text{cm}\\ \mathrm{r}=\frac{11}{2}=5.5\text{cm}\\ \mathrm{N}=1000\text{rev/min}\end{array}$

Use the formula for precession rate in terms of mass, gravitational acceleration, spin angular frequency, and moment of inertia to find out the precession rate.

Formula are as follow:

$\begin{array}{l}\mathbf{Ñ„}\mathbf{=}\frac{\mathbf{m}\mathbf{×}\mathbf{g}\mathbf{×}\mathbf{r}}{\mathbf{\pm õÓ\neg }}\\ \mathbf{Ó\neg }\mathbf{=}\mathbf{2}\mathbf{×}\mathbf{Ï€}\mathbf{×}\mathbf{f}\end{array}$

where,$\mathbf{f}$ is frequency, $\mathbf{m}$is mass, $\mathbf{g}$is acceleration due to gravity,$\mathbf{r}$ is radius, $\mathbf{I}$is moment of inertia,$\mathbf{Ó\neg }$ is angular frequency and$\mathbf{Ñ„}$ is precession rate.

To find precession rate, first find angular velocity as follows:

$\mathrm{Ó\neg }=2×\mathrm{Ï€}×\frac{\mathrm{N}}{60}$

Here, $N$ is the frequency in rpm,

$\mathrm{Ó\neg }=2×\mathrm{Ï€}×\frac{1000}{60}$

So,

$\mathrm{Ó\neg }=104.72\text{rad/s}$

Now, precession rate is given as,

$\begin{array}{l}\mathrm{Ñ„}=\frac{\mathrm{m}×\mathrm{g}×\mathrm{r}}{\mathrm{\pm õÓ\neg }}\\ \mathrm{Ñ„}=\frac{2×9.81×5.5×0.01}{{\left(0.5\right)}^2×104.72}\\ \mathrm{Ñ„}=0.041\text{rad/s}\end{array}$

Hence,precession rate of a gyroscope is${\text{0.041rad/sec}}^{\text{2}}$.

Therefore, using the concept of precession, the rate of precession and the direction in which the precession occurs can be found.