  Restoration of broken circular symmetry is used to explore the
characteristics of the ground states and the excitation spectra of rotating
Wigner molecules (RWM's) formed in two-dimensional parabolic N-electron quantum
dots. In high magnetic fields, the RWM's are floppy rotors with the energies of
the magic angular momentum (L) states obeying aL + b/L^{1/2}. Under such fields
the ground-state energies (referenced to the kinetic energy in the lowest
Landau level) approach the electrostatic energy of N point charges in the
classical equilibrium molecular configuration. At zero field and strong
interelectron repulsion, the RWM's behave like quasiclassical rigid rotors
whose energies vary as L^2. The particular L-dependence in high B is inherent
and natural to a floppy rotating WM, and it can be used as a crucial diagnostic
tool for resolving the recently posed question whether the composite-fermion or
the RWM picture is appropriate for QD's.
