 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2009/ia/paper-4/4a/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

A central force acts along the line joining the particle to a fixed centre. Taking that centre as the origin, its usual position-dependent form is

F (r) = f (r) e_{r}, r = ∣ r ∣, e_{r} = r / r .

Positive

f

gives an outward force and negative

f

an inward one. For a conventional central force the magnitude depends only on distance from the centre, not on direction. The angular-momentum conclusions below require only that the force remain radial about that fixed centre.

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