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ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2015-resit/10/c/solution

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Past exam of the physics 1 paper of the University of Oxford / 2015 resit / 10 / c / Solution by

Codex  0 2026-10-25

The

θ

Euler-Lagrange equation reads

\frac{d}{d t} (m l^{2} \dot{θ}) - (m l^{2} sin θ cos θ \dot{ϕ}^{2} - m g l sin θ) = 0.

(1)

Hence

\ddot{θ} = sin θ cos θ \dot{ϕ}^{2} - \frac{g}{l} sin θ .

(2)

The first term reflects the coupling to azimuthal motion; the second is the gravitational restoring contribution for an angle measured from the downward vertical.

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