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/Newtonian mechanics.org | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) (limited to 'mindmap/Newtonian mechanics.org') diff --git a/mindmap/Newtonian mechanics.org b/mindmap/Newtonian mechanics.org index c78b1e3..7d4b414 100644 --- a/mindmap/Newtonian mechanics.org +++ b/mindmap/Newtonian mechanics.org @@ -54,12 +54,13 @@ In general, the total momentum is defined to be: \end{align*} And in real life, we observe that things can transfer momentum. That is: \begin{align*} -\vec{p}_{1} = -\vec{p}_{2} +\vec{p}_{1} = -\vec{p}_{2} + \vec{p}_{i} \end{align*} -When these two objects have the same position vector \( \vec{r}_{1} = \vec{r}_{2} \) (if they are point masses; don't have volume but have mass which is idealistic but works as an approximation). -Because this operation of momentum transfer is symmetrical: +Where $\vec{p}_{i}$ is the initial momentum of the objects. +this happens when these two objects have the same position vector \( \vec{r}_{1} = \vec{r}_{2} \) (if they are point masses; don't have volume but have mass which is idealistic but works as an approximation). +This operation of momentum transfer is symmetrical: \begin{align*} -\vec{p}_{2} = -\vec{p}_{1} +\vec{p}_{2} = -\vec{p}_{1} + \vec{p}_{i} \end{align*} Note that the fact that this operation is symmetrical must be the case to preserve the property: \begin{align*} -- cgit