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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.11.17 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.



 

Jess H. Brewer - Last modified: Sat Nov 14 12:45:50 PST 2015