 Solution

ID: past-exam-of-the-short-options-paper-shared-by-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2019/s7/2/c/solution

Suppress primes on the angular velocity while retaining rotating components. The canonical momentum is

\partial L^{'} / \partial \dot{r}^{'} = m (\dot{r}^{'} + Ω \times r^{'})

. Varying

L^{'}

m \ddot{r}^{'} = - \nabla^{'} U^{'} - 2 m Ω \times \dot{r}^{'} - m Ω \times (Ω \times r^{'}) - m \dot{Ω} \times r^{'} .

The terms are the physical force, the velocity-dependent Coriolis force, the outward centrifugal force, and the Euler force caused by changing angular velocity. The common origin is inertial; an accelerating origin would introduce another translational apparent force.

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