First find the motion of the center of mass. Then work in the center of mass frame - you have 2 particles going in circles around the center of mass.
I am having trouble answering the question that follows:
Two particles, of mass m and 3m, are connected by a light rigid rod. The system rests on a smooth(no friction) horizontal table, the heavier mass due east of the lighter mass. The heavier mass is projected with initial velocity u directly north. Find the velocities of the particles when the rod runs north-south.
I have attached an image to clarify the setup. I would really appreciate an explanation of how to do it or even just any help you can give.