Abstract
In this paper, we work with teleparallel gravity and show that the values of the torsion vector and the torsion axial-vector depend on the choice of the tetrad field. We choose two different sets of tetrad fields, each of them satisfies the tetrad's conditions and leads to the Van Stockum spacetime. We obtain expressions for the torsion vector and the torsion axial-vector. In addition, we found that the obtained expressions are quite different for the two sets of tetrad fields. For the spacetime under consideration, if the metric coefficients are assumed to be functions of t only, it is then shown that the torsion axial-vector vanishes completely and the torsion vector still depends on the choice of tetrad fields. Finally, we found the spin precession of a Dirac particle in the spacetime under consideration.