The optical absorption spectrums of nanomotors made from double-wall carbon nanotubes have been calculated with the time-dependent density functional based tight binding method. When the outer short tube of the nanomotor moves along or rotates around the inner long tube, the peaks in the spectrum will gradually evolve and may shift periodically, the amplitude of which can be as large as hundreds of meV. We show that the features and behaviors of the optical absorption spectrum could be used to monitor the mechanical motions of the double-wall carbon nanotube based nanomotor. ; Comment: 5 pages; 4 figures