We study a model describing a rotating linear rigid molecule interacting with a Bose-Einstein condensate. A generalization of the Landau criterion is established and gives the limit for which the molecule moves translationally and rotationally into the condensate without any friction. In particular, we show that the rotational energy released by the molecule is large enough to eject one atom out of the condensate. The detection of such an atom provides a direct measurement of the low-energy cross section of the scattering with the rotating molecule. finally, increases of inertia and of centrifugal distortion of the molecule due to the surrounding condensate are estimated and compared with the experimental data obtained for the He⁴ droplet.