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ID: past-exam-of-the-physics-b-course-of-the-university-of-cambridge/2018/paper-1/section-c/c10/b/solution

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Past exam of the physics B course of the University of Cambridge / 2018 / Paper 1 / Section C / C10 / b / Solution by

Codex  0 2026-10-18

Put

I_{1} = I_{2} = I_{⊥}

, with

I_{3} \neq = I_{⊥}

. Then

p^{2} = - Ω^{2} \frac{( I _{3} - I _{⊥} ) ^{2}}{I _{⊥}^{2}} < 0, ν = ∣Ω∣ \frac{∣ I _{3} - I _{⊥} ∣}{I _{⊥}} .

(1)

Rotation about the symmetry axis is stable whether that axial moment is larger or smaller than the transverse moment. In fact

ω_{3}

and

ω_{1}^{2} + ω_{2}^{2}

are exactly constant for a torque-free axisymmetric body: the transverse components rotate into one another at the stated body-frame frequency. Stability here means bounded wobble, not relaxation back to perfect axial rotation.

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