I have a uniform rod of mass M, which rotates about one of its ends, and a point mass equal to the mass of the rod is added to the other end. To calculate the new moment of inertia, do I just need to add the moment of inertia of the rod and that of the point mass together? i.e. I = (MR^2)/3 + MR^2 ? Any help would be much appreciated.
Yes you add them together, but make sure you add them together with respect to the same axis. Remember the parallel axis theorum.