When dealing with central forces, we can find the energy of a particle under the influence of such a force to be E=0.5m(dr/dt)2+(L2/2mr2)+U(r). We define the effective potential as the sum of the last two terms. In my previous experience of dealing with energy considerations to predict motion, analysis of the potential function U(r) has been sufficient. But with central forces it seems necessary to consider Ueff(r). Why is this - why can't I just consider U(r) alone? I can't really find anywhere that properly explains why we need to use it. Thanks.