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

[Dixanadu]

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!

 

[robphy]

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]

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]

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.