Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 14A / c / Solution

The radial effective potential is $V_{\mathrm{eff}}=mgr\cot \alpha +5J^2/(14m{r}^2)$. Initially $r=8a$, $J=(7m/5)(8a)v_0$. Comparing the initial energy with $V_{\mathrm{eff}}(2a)$ giveswhich is exactly $v_0^2\ge (4/7)ga\cot \alpha$. Larger speed raises the centrifugal barrier at the neck faster than it raises the initial kinetic energy.