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

• I
Hi guys,

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

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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Gold Member
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.

dextercioby
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.

PeroK
Homework Helper
Gold Member
Hi guys,

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

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.