For a steady motion, no acceleration, the torque only needs to be enough to over come friction in the bearings.
But, to go from stopped to some speed, acceleration, the torque needs to over come the mass inertia of the weights and the same torque but opposite, to stop the motion.
If each mass 5kg and the total arm length is 2m. Then the torque required = length * mass * acceleration(tangential) + bearing frictional force * bearing radius.
The equations can be found in any first year physics text.