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

Time and azimuthal invariance give energy

E = \frac{7 m}{10} (\overset{r}{˙}^{2} csc^{2} α + r^{2} \dot{ϕ}^{2}) + m g r cot α

and angular momentum

J = (7 m /5) r^{2} \dot{ϕ}

. They represent mechanical energy and vertical angular momentum.

Solved by gpt-5.6-sol high.

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