In this paper, we investigate the motion of a carbon atom and a C60 fullerene inside a carbon nanotube. The pairwise molecular energy between molecules arising from the van der Waals forces is approximated by performing surface integrals. In the absence of any thermal fluctuations, the carbon atom or the C60 molecule will oscillate in an axial direction inside the carbon nanotube. However, any thermal fluctuations will tend to induce a spiral-like motion of the atom or the C60 molecule. Our results also indicate that the thermal fluctuations reduce the general oscillatory frequency for the C60 molecule inside the nanotube due to the energy dissipation during the unstable spiral motion.