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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2011/ia/paper-4/10b/solution

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Past exam of the mathematics course of the University of Cambridge / 2011 / ia / Paper 4 / 10B / Solution by

Codex  0 2026-10-14

Apply the rotating-frame derivative formula first to position and then to its inertial velocity:

(\frac{d r}{d t})_{I} = \dot{r} + ω \times r,

(\frac{d ^{2} r}{d t ^{2}})_{I} = \ddot{r} + 2 ω \times \dot{r} + ω \times (ω \times r) .

The angular velocity is constant, so there is no term involving

\dot{ω}

. By Newton's second law in the inertial frame, the inertial acceleration is

F / m

. Rearrangement gives the equation of motion in a rotating frame:

m \ddot{r} = F - 2 m ω \times \dot{r} - m ω \times (ω \times r) .

The two additional accelerations are the Coriolis acceleration and centrifugal acceleration.

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