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define central forces
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DEFINE OF CENTREL FORCE
In classical mechanics, a central force on an object is a force that is directed along the line joining the object and the origin:[a][1]
In classical mechanics, a central force on an object is a force that is directed along the line joining the object and the origin:[a][1]{\displaystyle {\vec {F}}=\mathbf {F} (\mathbf {r} )=F(\mathbf {r} ){\hat {\mathbf {r} }}}{\displaystyle {\vec {F}}=\mathbf {F} (\mathbf {r} )=F(\mathbf {r} ){\hat {\mathbf {r} }}}
In classical mechanics, a central force on an object is a force that is directed along the line joining the object and the origin:[a][1]{\displaystyle {\vec {F}}=\mathbf {F} (\mathbf {r} )=F(\mathbf {r} ){\hat {\mathbf {r} }}}{\displaystyle {\vec {F}}=\mathbf {F} (\mathbf {r} )=F(\mathbf {r} ){\hat {\mathbf {r} }}}where {\displaystyle \scriptstyle {\vec {\text{ F }}}} \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 {\displaystyle \scriptstyle {\hat {\mathbf {r} }}} \scriptstyle \hat{\mathbf{r}} = r/||r|| is the corresponding unit vector.
In classical mechanics, a central force on an object is a force that is directed along the line joining the object and the origin:[a][1]{\displaystyle {\vec {F}}=\mathbf {F} (\mathbf {r} )=F(\mathbf {r} ){\hat {\mathbf {r} }}}{\displaystyle {\vec {F}}=\mathbf {F} (\mathbf {r} )=F(\mathbf {r} ){\hat {\mathbf {r} }}}where {\displaystyle \scriptstyle {\vec {\text{ F }}}} \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 {\displaystyle \scriptstyle {\hat {\mathbf {r} }}} \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.
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