Past exam of the mathematics course of the University of Oxford / 2021 / Prelims / Mathematics IV / 6 / a

All time derivatives in this part are taken relative to the rotating reference frame, so its basis is held fixed during differentiation. Put $f(\varphi )=p(\varphi )\sin \varphi$ and $q(\varphi )=p(\varphi )\cos \varphi$. The chain rule and product rule giveExplicitly,The separate Coriolis force and centrifugal force terms in the stated equation account for the motion of the basis relative to an inertial observer.