If there are two turning points such that the radius r is bounded between r min and r max, then the motion is contained within an annulus of those radii. As the radius varies from the one turning point to the other, the change in azimuthal angle φ equals Δ Δ φ φ = L 2 m ∫ ∫ r min r max d r r 2 E − − U ( r ) − − L 2 2 m r 2