single rigid body with $$\omega_1 = \omega_2 = \omega_o, \eqno(3)$$

we have

$$E = \frac{1}{2}\left[6mr_o^2\omega_o^2 + 
48mr_o^2\omega_o^2\right] = \frac{1}{2}\left[54mr_o^2\omega_o^2\right]  
= \frac{1}{2}I\omega_o^2 \quad \quad {\rm or} \quad I = 54mr_o^2. \eqno(4)$$

Since the condition of constant angular momentum, applied to two atoms moving on different orbits of radius $r_1$ and $r_2$ ([*cf.*]{}, Fig.2B) renders $$mr_1^2\omega_1 = mr_2^2\omega_2  = C \quad ({\rm constant}) 
\quad \quad {\rm or} \quad 
\omega \propto r^{-2}, \eqno(5)$$

which implies that corresponding linear velocity $v = r\omega$ changes as $r^{-1}$. As expected, this agrees with the well known dependence of $v$ on $r$ in a quantum vortex observed in superfluid $^4$He [@wilks]. Using Eqn.(5) in Eqn.(1), we get

$$E = \frac{1}{2}\left[6mr_1^2\omega_1^2 +  
12mr_2^2\omega_1^2\left(\frac{r_1}{r_2}\right)^4\right]  \eqno(6)$$

which for the orbits satisfying Eqn.(2) and $\omega_1 = \omega_o$ renders

$$E = \frac{1}{2}\left[6mr_o^2\omega_o^2 + 
12mr_o^2\omega_o^2\frac{1}{4}\right] \quad =
\frac{1}{2}\left[9mr_o^2\omega_o^2\right]; \quad \quad 
{\rm with} \quad I = 9mr_o^2. \eqno(7)$$

Eqn.(6) clearly reveals that the contribution to $I$ from an atom at a distance $r_2$, under the condition of constant angular momentum (Eqn. 5), gets reduced by a significant factor of $(r_1/r_2)^4$ (since $r_1 < r_2$) in comparison to that found under the condition of constant angular velocity (Eqn.(4)). As an example, the contribution to $I$ 