marsultor/warehouse
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

some more vector stuff

Browse Source
This commit is contained in:
Krishna
2024-08-22 20:11:23 -05:00
parent 123b216b90
commit 772acaeaae
1 changed files with 14 additions and 3 deletions
Download Patch File Download Diff File Expand all files Collapse all files

17
content/physics/kinematics.md
View File

@@ -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