Past exam of the mathematics course of the University of Cambridge / 2021 / ia / Paper 4 / 10C / b / Solution

Motion under a central force is planar. In plane polar coordinates, the radial component of the acceleration is $\ddot{r}-r{\dot{\theta }}^2$, soThe conserved specific angular momentum is $h=r^2\dot{\theta }$. Substitution of $\dot{\theta }=h/r^2$ yieldsThe last term is the centrifugal part of the radial effective potential.