Based on the Hellman-Feynman theorem, it is shown that the average squ
are radius of a cloud of interacting bosons in a parabolic well can be
derived from their free energy. As an application, the temperature de
pendence of the moment of inertia of noninteracting bosons in a parabo
lic trap is determined as a function of the number of bosons. Well bel
ow the critical condensation temperature, the Bose-Einstein statistics
are found to substantially reduce the moment of inertia of this syste
m, as compared to a gas of ''distinguishable'' particles in a paraboli
c well.