91Ó°ÊÓ

$\begin{array}{c}\mathrm{f}=3\text{0rev/sec}\\ \mathrm{m}=0.5\text{kg}\\ \text{I}=5×{10}^{−4}\text{kg}.{\text{m}}^2\\ \mathrm{r}=0.04\text{m}\end{array}$

Use 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.

(a)

$\begin{array}{l}\mathrm{Ó\neg }=2×\mathrm{Ï€}×\mathrm{f}\\ \mathrm{Ó\neg }=2\mathrm{Ï€}×30\\ \mathrm{Ó\neg }=188.4\text{9rad/sec}\end{array}$

Now,

$\begin{array}{l}\mathrm{Ñ„}=\frac{\mathrm{m}×\mathrm{g}×\mathrm{r}}{\mathrm{\pm õÓ\neg }}\\ \mathrm{Ñ„}=\frac{0.5×9.81×0.04}{5×{10}^{−4}×188.49}\\ \mathrm{Ñ„}=2.0\text{8rad/sec}\end{array}$

Hence, precession rate is $2.08{\text{rad/s}}^{\text{2}}$.

(b)

The direction of precession rate is clockwise which can be seen from above.

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