the influence of its rotation.

The fact, that different atoms on different concentric circles around the axis of a quantum vortex in He-II move coherently in order of their locations in a manner that they have no difference in their angular momentum [@wilks] implies that their angular velocity ($\omega$) changes as $r^{-2}$ where $r$ is the distance of the atom from the axis of the vortex. This differs from atoms of a rigid body rotor where all atoms move around the axis of rotation with identically equal $\omega$. In the following we consider the example of a set of $^4$He atoms moving on two concentric circles around the axis of rotation (as shown in Fig.2A) under the condition of: (i) constant angular velocity and (ii) constant angular momentum. To this effect we evaluate the kinetic energy of the set by using, $$E = \sum_i^6\frac{n_i}{2}mr_1^2\omega_1^2 +  
\sum_j^{12}\frac{n_j}{2}mr_2^2\omega_2^2,  \eqno(1)$$

where we have $n_i = 1, 2, 3, ...6$ and $n_j = 1, 2, 3, ...12$ with indices $i$ and $j$ to identify different atoms on orbits 1 and 2, respectively. Presuming that the radii of orbits 1 and 2 satisfy $$r_2 = 2r_1 = 2r_o \eqno(2)$$

and all atoms move as a 