Final answer:
The angular momentum of a two-particle system with equal mass and opposite velocities is conserved and identical regardless of the reference point due to the absence of external torques and the principle of angular momentum conservation.
Step-by-step explanation:
The question concerns angular momentum and its conservation in a physical system. Specifically, it asks to demonstrate that the angular momentum of a two-particle system is conserved, regardless of the reference point chosen for the calculation, when two particles of equal mass move with the same speed in opposite directions separated by a distance d.
The total angular momentum of a system remains constant provided there is no external torque acting on the system, just as the total linear momentum remains constant when no external force is present.
Angular momentum L is given by L = Iw, where I is the moment of inertia and w is the angular velocity. In the case of the two-particle system, each particle contributes to the total angular momentum, but as they are equal in mass and moving at equal speeds in opposite directions, their angular momenta have the same magnitude but opposite directions.
Since no external torques are introduced, any internal changes cancel each other out, keeping the total angular momentum of the system constant.