 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2018/s7/2/c/solution

Use the conserved

p_{ϕ} = p_{ψ} = I_{3} ω

in the canonical-momentum equation. For a nonzero tilt,

I_{1} \dot{ϕ} sin^{2} θ = I_{3} ω (1 - cos θ) .

Cancelling with the half-angle identities gives

\dot{ϕ} = \frac{I _{3} ω}{I _{1} ( 1 + cos θ )} = \frac{C}{2 cos ^{2} ( θ /2 )} .

Its regular limit at the north pole is

C /2

, although the azimuth itself is not a uniquely defined coordinate at that pole.

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