 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-1/39b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

The outer circle obeys

x^{2} + (y - 2 a)^{2} = (2 a)^{2}

, and hence

r = 4 a sin θ .

Its counterclockwise tangent is again

(cos 2 θ, sin 2 θ)

- Ω/4

and radius is

2 a

, so its signed tangential speed is

- a Ω/2

ψ = 0, u_{r} cos θ + u_{θ} sin θ = - \frac{a Ω}{2} at r = 4 a sin θ .

The first follows both from impermeability and from the common streamfunction value forced by the contact point.

 New to topics? Read the docs here!