Problem $1$: Problem $4\mathrm{.}45$ in the text.

Exercise $4\mathrm{.}45$

The disk is rolling without slipping over the horizontal XY plane. At the instant when the angle of inclination is $=30,$ the disk is observed to be spinning at ${}^{}=5ra\frac{d}{s}.$ At this instant, the speed of points $B$ and $C$ on its horizontal diameter are $1$ and $2\frac{m}{s},$ respectively. Determine the corresponding precession and nutation rates.