Past exam of the probability, statistics and options I course of the University of Oxford / 2009 / H / 1 / iii / Solution

The derivative of the pair's total angular momentum is $q_1\times F-q_2\times F=(q_1-q_2)\times F=0$, since $F$ is parallel to the separation vector. Therefore the combined angular momentum of particles one and two is conserved, despite the possible exchange between them individually.