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Central force
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Description
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
→
=
F
(
r
)
=
|
F
(
r
)
|
r
^
{\displaystyle {\vec {F}}=\mathbf {F} (\mathbf {r} )=\left\vert F(\mathbf {r} )\right\vert {\hat {\mathbf {r} }}}
where
F
→
{\displaystyle \scriptstyle {\vec {\text{ 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
r
^
{\displaystyle \scriptstyle {\hat {\mathbf {r} }}}
= r/||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.
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