A model set of equations including Brownian rotation dynamics is proposed to investigate the role of rotation on the drift velocity of nanorods in the direction of an external field (such as electrical). Both inertial and non-inertial Brownian rotation are considered and the more realistic non-inertial shows more correlation between the rotational and translational motion. The average drift velocity is computed from the spatial trajectory for each path and the ensemble average and its confidence interval are computed from the average of 300 trajectories. The key parameter for the trajectories is the maximum rotational stopping distance, θSt. For a value of about 0.6 radians and a length of about 60 nm, the nanorod velocity is midway between the limiting value for the large and small value of θSt. The reduced velocity is found to depend on the length of the nanorod but not the diameter. A method of estimating the 3D observed mobility from the 1D simulations based on the reduced velocity is proposed. The experimental results of Gopalakrishnan et al. (2015) for 200 nm gold nanorods are consistent with an enhancement from rotation coupling for the gold nanorods 200 nm long in the free molecule limit. The effect of an elastic collision boundary condition is also considered.