Consider a particle of mass m moving in two dimensions between two perfectly reflecting walls which intersect at an angle alpha at the origin. Assume that when the particle is reflected, its speed is unchanged and its angle of incidence equals its angle of reflection. The particles is attracted to the origin by a potential U(r)=-c/r^3 where c is some constant and r is the distance of the particle to the origin. Now start the particle at a distance R from the origin on the x-axis with a speed v and initial angle with x-axis theta. Show that the magnitude of the angular momentum is conserved when it reflects off a wall. Show that the angular momentum of the particle is conserved in between collisions (i.e. when the particle is moving in free space under the potential field U(r)). Determine the equation for distance of the closest approach to the origin.