Past exam of the mathematics course of the University of Cambridge / 2009 / ia / Paper 4 / 4A / a

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 isPositive $f$ 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.