In the following scenarios, state what (if any) the conserved quantities of the system are (e.g. momentum of the center of mass, or a component of angular momentum). Justify your answer in a way that another physics grad student could understand. a) A system of particles at positions r, is acted upon by forces F; parallel to the z-axis. What if the r; lie only the xz plane? b) A system of two particles which interact with potential V(x1,2) = (X X) -