Central force

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.^: 93

{\vec {F}}=\mathbf {F} (\mathbf {r} )=\left\vert F(\mathbf {r} )\right\vert {\hat {\mathbf {r} }}

where ${\textstyle {\vec {F}}}$ is the force, F is a vector valued force function, F is a scalar valued force function, r is the position vector, ||r|| is its length, and ${\textstyle {\hat {\mathbf {r} }}=\mathbf {r} /\|\mathbf {r} \|}$ is the corresponding unit vector.

Not all central force fields are conservative or spherically symmetric. However, a central force is conservative if and only if it is spherically symmetric or rotationally invariant.^: 133–38

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