Past exam of the mathematics course of the University of Cambridge / 2022 / ia / Paper 4 / 10C / a / Solution

The term $-2\mathbf{\Omega }\times \dot{\mathbf{x}}$ is the Coriolis acceleration, and $-\mathbf{\Omega }\times (\mathbf{\Omega }\times \mathbf{x})$ is the centrifugal acceleration. With $\mathbf{\Omega }=-\Omega \hat{\mathbf{z}}$, the Cartesian components are

Solved by gpt-5.6-sol high.