From 772acaeaae1cd6836a875ce8ece2c672160190a1 Mon Sep 17 00:00:00 2001 From: Krishna Date: Thu, 22 Aug 2024 20:11:23 -0500 Subject: [PATCH] some more vector stuff --- content/physics/kinematics.md | 17 ++++++++++++++--- 1 file changed, 14 insertions(+), 3 deletions(-) diff --git a/content/physics/kinematics.md b/content/physics/kinematics.md index 217dba5..3843836 100644 --- a/content/physics/kinematics.md +++ b/content/physics/kinematics.md @@ -87,8 +87,11 @@ Just remember that $g=9.80\mathrm{m}/\mathrm{s}^2$ You haven't seen any vectors to this point yet, so here we go! Vectors are essentially made of 2 components as long as they are two dimensional. You can either specify the relative coordinates they meet or the direction and magnitude. For example, you can write it out as either: $\vec{p}=\langle a,b\rangle$ or as $\vec{p}=\langle m;\theta \rangle$. To convert between them: $\vec{p}=\langle m\sin{\theta},m\cos{\theta}\rangle$ ## Adding and Subtracting Vectors: -![](https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2Fmedia.nagwa.com%2F124176839832%2Fen%2Fthumbnail_l.jpeg&f=1&nofb=1&ipt=408b463f7b54ff9a5f32090ae4fdb5581a1d425798af862a483c121bdedeae94&ipo=images) -Now that you understand that, I can say that displacement in 2D is all about a certain amount of movement in $\hat{i}$ direction or $\hat{j}$, then adding or subtracting them to compute the same dimensional cumulative vector. +![](https://external-content.duckduckgo.com/iu/?u=https%3A%2F%2Fmedia.nagwa.com%2F124176839832%2Fen%2Fthumbnail_l.jpeg&f=1&nofb=1&ipt=408b463f7b54ff9a5f32090ae4b5581a1d425798af862a483c121bdedeae94&ipo=images) +Now that you understand that, I can say that displacement in 2D is all about a certain amount of movement in $\hat{i}$ direction or $\hat{j}$, then adding or subtracting them to compute the same dimensional cumulative vector. Anywyas, Adding them is as simple as arranging the vectors tail to tip, and then the next tail to tip. Then you compute the vecor formed between the exposed tail and tip. Algebraically, it looks like this: +$$ +\langle a,b \rangle + \langle c,d \rangle = \langle a+c,b+d \rangle +$$ ## Magnitude For the rectangular component vector form: @@ -101,6 +104,14 @@ $$ $$ Refer to the stuff above to make sense of this. -## 2D Kinematics +## Multiplying a vector and a scalar +$$ +c\vec{p}=c\langle a,b \rangle=\langle ca,cb \rangle +$$ +# 2D Kinematics + +## Calculating Displacement in 2D +The displacement vector $\vec{D}$ is simply the sum off all movement vectors $\vec{m_{0 \ldots n}}$. You can the calculate the magnitude of that vector to get the distance of the displacement as $||\vec{D}||$ + #physics