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ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2019-resit/11/a/solution

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Past exam of the physics 1 paper of the University of Oxford / 2019 resit / 11 / a / Solution by

Codex  0 2026-10-25

About a fixed origin in an inertial frame, the angular momentum and torque are

L = r \times m v, τ = r \times F .

For a specified fixed axis with unit vector

n

, use the projections

L_{n} = n \cdot L

and

τ_{n} = n \cdot τ

. The mass is constant. Differentiating and applying Newton's second law,

\frac{d L}{d t} = v \times m v + r \times m \dot{v} = 0 + r \times F = τ .

Hence

\dot{L}_{n} = τ_{n}

for the fixed axis. If the net torque vanishes, the corresponding angular momentum is conserved. Fixing the origin and axis is essential to this unmodified form of the law.

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