I'm having trouble with RHK12-28. I tried considering the rod as having two different torques on it and then I would solve for angular accel, but since the rod has no mass it has no moment of inertia, and that screws the calculations up. And I tried assuming the two masses to be fixed to the rod and not hanging, but that didn't work either...
The problem is easier but the physics does not change if you take the masses to be attached directly to the end of the rod rather than hanging by strings. (Note that this is only true because they are hanging by strings -- if they were attached by rigid links then you would need to know the distance of each mass below the rod.) Then the moment of inertia is m*(L1)^2 + m*(L2)^2.