An Egg With $B$ood...

$F^{*}_c=F_{drag}sin(\theta)=\delta m.r.\omega^2$

$\omega^2=\cfrac{F_{drag}}{\delta m}\cfrac{sin(\theta)}{r}$

where ${F_{drag}}$ is a force not the distance from the origin to the elemental mass, $\delta m$ on the surface of the particle.  The particle will deform such that it rotates as a whole at a constant angular velocity.

$\omega^2=A.{F_{drag}}$

 $A$ is a constant.

If we define that when the particle spins at $\omega_o$ , it will present an $S_n=38.5$, and that $\omega$ is proportional to $S_n$,

$\cfrac{\omega}{\omega_o}=\cfrac{S_n}{38.5}$

And we consider that the particle starts at $S_n=39$ when $\omega=0$, spinning decreases $S_n$ and at $\omega=\omega_o$,  $S_n=38.5$, we have,

$S_n=39-0.5\cfrac{\omega}{\omega_o}$

$S_n=39-\cfrac{0.5}{\omega_o}\sqrt{AF_{drag}}$

as $F_{drag}\propto v^2$

$S_n=39-\cfrac{0.5S}{\omega_o}v$

where $S$ is a constant.

where $\omega\le\omega_o$.  And we define $\omega_o$ to be the the maximum angular velocity attained by the particle as $B$ oscillates, assuming that the particle does not continue to increase in spin when $S_n=38.5$.

Are we ready to make $B$ spin?  It is Bu...ood as in wood.