Is there a name for this fact in physics? is it a theorem?

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  • Thread starter Dixanadu
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Hi guys,

So just wondering - the fact that the force is always the negative derivative of potential with respect to distance:
[itex]F=-\dfrac{\partial V}{\partial x}[/itex]

Where does this come from and does it have a name or something? like a theorem perhaps?

Thanks!
 

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robphy
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Such a force is called a "conservative force", a "force derivable from a potential energy function".
However, not all forces are like this... for example, kinetic friction force is not of this type.
 
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dextercioby
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It is not a theorem in physics, but one in mathematics called "the lemma of Poincare", which, when applied to R^3, states that any conservative vector field (thus defined to have a 0 circulation along a closed path, equivalently having 0 curl) is the gradient of a scalar field we call potential.
 
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PeroK
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Hi guys,

So just wondering - the fact that the force is always the negative derivative of potential with respect to distance:
[itex]F=-\dfrac{\partial V}{\partial x}[/itex]

Where does this come from and does it have a name or something? like a theorem perhaps?

Thanks!
The equivalent in Quantum Mechanics is called the Ehrenfest Theorem. There's lots about that online.
 

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