Central force in the context of Conservative 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.$${\displaystyle \mathbf {F} (\mathbf {r} )=F(\mathbf {r} ){\hat {\mathbf {r} }}}$$where F is a force vector, 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 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. Examples of spherically symmetric central forces include the Coulomb force and the force of gravity.