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.^[a][1]: 93 $${\displaystyle {\vec {F}}=\mathbf {F} (\mathbf {r} )=\left\vert F(\mathbf {r} )\right\vert {\hat {\mathbf {r} }}}$$ 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.^{[1]: 133–38}

Cite error: There are <ref group=lower-alpha> tags or {{efn}} templates on this page, but the references will not show without a {{reflist|group=lower-alpha}} template or {{notelist}} template (see the help page).