The radial motion in three dimensions in a spherically symmetric potential is just like motion in one dimension. The following discussion of motion in one dimension can be usefully extended to the radial motion in a spherically symmetric potential, if we replace the potential by the effective potential. $$ V (x) \longrightarrow V_{eff} (r) = V (r) + \frac {L^2} {2mr^2} \hspace{5em} (17) $$ Thus for motion in three dimensional spherically symmetric potential $$ E = \frac 1 2 m {\dot r}^2 + V_{eff} (r). \hspace{5em} (18) $$ **4.1 Nature of Orbits** 1. Conservation of angular momentum implies the motion of particle is in a plane 2. If angular momentum is zero, \( \vec r × \vec p = 0. \Longrightarrow \vec r \) and \( \vec p \) are parallel. In this case the particle moves in a straight line. 3. If angular momentum is nonzero, the bounded or unbounded nature of the orbit can be