Central force

Mechanical force towards or away from a point

In classical mechanics, a central force on an object is a force that is directed towards or away from a point called center of force. F ( r) = F ( r) r ^ {\displaystyle \mathbf {F} (\mathbf {r})=F(\mathbf {r}){\hat {\mathbf {r} }}} where F {\displaystyle \mathbf {F} } is a force vector, F {\displaystyle F} is a scalar valued force function (whose absolute value gives the magnitude of the force and is positive if the force is outward and negative if the force is inward), r {\displaystyle \mathbf {r} } is the position vector, ‖ r ‖ {\displaystyle \|\mathbf {r} \|} is its length, and r ^ = r / ‖ r ‖ {\textstyle {\hat {\mathbf {r} }}=\mathbf {r} /\|\mathbf {r} \|} is the corresponding unit vector. Not all central force fields are conservative or spherically symmetric.

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