From a7da57c0736bec58d1fc4ec99d211099c31bb45f Mon Sep 17 00:00:00 2001 From: Preston Pan Date: Wed, 24 Jan 2024 19:26:59 -0800 Subject: new content --- mindmap/conservative force.org | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'mindmap/conservative force.org') diff --git a/mindmap/conservative force.org b/mindmap/conservative force.org index 83d1c36..9b01117 100644 --- a/mindmap/conservative force.org +++ b/mindmap/conservative force.org @@ -15,7 +15,7 @@ A conservative force has this property: \end{align*} In other words, work done by \(\vec{f}\) is path independent, because in any closed loop integral, you go from point \(\vec{a}\) to point \(\vec{b}\) and then back. If these forwards and backwards -paths end up canceling no matter what path you take, then it is clear that \(\vec{f}\) will do the +paths end up canceling no matter what path you take, then it is clear that \(\vec{f}\) will be the same amount of force no matter what path you take. Using Stokes' theorem: \begin{align*} \int_{S}(\vec{\nabla} \times \vec{f}) \cdot d\vec{a} = \oint\vec{f} \cdot d\vec{l} -- cgit