= Solution
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
$$
\boxed{\mathbf F(\mathbf r)=f(r)\,\mathbf e_r,\qquad r=|\mathbf r|,\quad\mathbf e_r=\mathbf r/r.}
$$
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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