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Central Forces

Many [maybe even most] forces in nature are directed toward [or away from] some ``source'' of the force. An obvious example is Newton's Universal Law of Gravitation, but there are many others evident, especially in elementary particle physics.<sup>11.17</sup> We call these forces ``central'' because if we regard the point toward [or away from] which the force points as the centre (or origin  O) of our coordinate system, from which the position vector   $\mbox{\boldmath$\vec{r}$\unboldmath }$  is drawn, the cross product between   $\mbox{\boldmath$\vec{r}$\unboldmath }$  and   $\mbox{\boldmath$\vec{F}$\unboldmath }$  (which is along  $\hat{r}$) is always zero. That is,

``A central force produces no torque about the centre; therefore the angular momentum about the centre remains constant under a central force.''

This is the famous Law of CONSERVATION OF ANGULAR MOMENTUM. Note the limitation on its applicability.