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# Formulas!

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For a while i have been trying to make a blog with every one of the equations that we use. and then people can post comments with the ones that i am missing - and i'll edit it (or if that isnt a setting, mr. fullerton could) so that we can make a colaboration of every possible formula to study from. I was planning on doing this before midterms... but the equation editor would not work for me. its working now though... so here it goes (im sure i will miss a ton but its worth a shot)

MECHANICS

Notation

$A \cdot B=\left | A \right |\left | B \right |cos\theta$

$A \cdot B=A_{_{x}}B_{x}+A_{y}B_{y}+A_{z}B_{z}$

$A \times B=ABsin\theta$

Kinematics

$x =v_{i}t+\frac{1}{2}at^{2}$

$v^2 _ {f}={v_{i}}^{2}+2ax$

$a=\frac{v_{f}-v_{i}}{t}$

$x=v_{avg}t$

$v_{f}=v_{i}+at$

$v=\frac{dx}{dt}$

$a=\frac{dv}{dt}$

$x=\int vdt$

$v=\int adt$

Dynamics & Energy

$KE=\frac{1}{2}mv^{2}$

$PE=mgh$

$v=\sqrt{2gh}$

$w=Fxcos\theta$

$PE_{sping}=\frac{1}{2}kx^{2}$

$F_{spring}=-kx$

$w=\int F®dr$

$P=\frac{w}{t}$

$P=\frac{dw}{dt}$

$F=ma$

$F=\frac{d\rho }{dt}$

$\rho =m\Delta v$

$J=f\Delta t$

$P=Ft$

$F_{g}=\frac{Gm_{1}m_{2}}{r^{2}}$

$U_{g}=\frac{-Gm_{1}m_{2}}{r}$

$W=mg$

$w=\Delta KE$

$F_{friction}=\mu F_{N}$

Rotational Motion

$I_{}\parallel =I_{center}+ML^{2}$

$I_{z}=I_{x}+I_{y}$

$I=\int r^{2}dm$

$a=\alpha r$

$v=\omega r$

$x=\theta r$

$\theta =\omega t+\frac{1}{2}\alpha t^{2}$

${\omega _{f}}^{2}={\omega _{i}}^{2}+2\alpha \theta$

$\alpha =\frac{\omega _{f}-\omega _{i}}{t}$

$\tau =r\times F$

$L=r\times \rho$

$\tau = \frac{dL}{dt}$

$L=I\omega$

$w=\int \tau (\theta )d\theta$

$P=\tau \omega$

$F_{c}=\frac{mv^{2}}{r}$

$a_{c}=\frac{v^{2}}{r}$

$a_{c}=\omega ^{2}r$

$\tau =I\alpha$

$\Sigma \tau _{cw}=\Sigma \tau _{ccw}$

$KE_{rotational}=\frac{1}{2}I\omega ^{2}$

$w=\tau \theta$

$\tau =tr$

Specific Moment of Inertias

Cylinder

$\frac{1}{2}mr^{2}$

Hollow Cylinder

$\frac{1}{2}m({r_{1}}^{2}+{r_{2}}^{2})$

Solid Sphere

$\frac{2}{5}mr^{2}$

Hollow Sphere

$\frac{2}{3}mr^{2}$

Rod around Center

$\frac{1}{12}mr^{2}$

Rod around end

$\frac{1}{3}mr^{2}$

Simple Harmonic Motion

$T=\frac{2\pi }{\omega }$

$T_{pendulum}=2\pi\sqrt{\frac{l}{g}}$

$T_{spring}=2\pi\sqrt{\frac{m}{k}}$

$\theta =Acos(\omega t +\phi )$

$\omega =\sqrt{\frac{k}{m}}$

$\frac{d^{2}y}{dx^{2}}+\frac{k}{m}y=0$

ELECTRICTY & MAGNETISM

Electrostatics

$F=\frac{kq_{1}q_{2}}{r^{2}}=\frac{1}{4\pi \epsilon _{0}}\frac{q_{1}q_{2}}{r^{2}}$

$E=\frac{F}{q}$

$\lambda =\frac{Q}{L}$

$\sigma =\frac{Q}{A}$

$\rho =\frac{Q}{V}$

$d\phi = E\cdot \hat{n}dA=EdAcos\theta$

$\phi =VAcos\theta$

$\phi =\oint \underset{E}{\rightarrow}\cdot \underset{da}{\rightarrow}=\frac{Q_{enclosed}}{ \epsilon _{0}}$

Please let me know if i'm missing things. also if its better i could edit this so that energy and dynamics were 2 seperate categories. I know we got a formula sheet in the beggining of the year, but there isnt everything on their, and it's not really in any order... so lets compile a better list!

## Recommended Comments

i figured out how to edit and delete things, so Mr. Fullerton doesn't have to mod my posts everytime i make a mistake

feedback is appreciated. if i wrote done an equation wrong, or missed anything please let me know - i want to compile a full & accurate list!

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Also, i think i'm going to add in a section with all the specific moment of inertias. that'd be a good thing to study

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Great idea moe.ron!!! I think this will be a terrific asset for your class as well as classes to come. Perhaps when it's finished we can blow it up into a giant poster too.

Question... $\color \tau =tr$ did you mean to write Fr for the torque in this equation?

Thanks for this valuable post!

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i meant T as in tension... that should that be uppercase shouldnt it. or should i just use F instead?

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maybe I'm jumping the gun but what about good 'ol QVC?

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Sweeeet! Only one thing that I saw, although I think you should keep it. You wrote PE of a sping.

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haha blake yeah im not editing that right now but maybe i will later.

and yeah Will... notice at the top it says: MECHANICS

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i'll do an E&M formula sheet before the AP

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Everyone do yourselves a favor and rate this blog like its a five star hotel. It will be easier to find at the end of the year when we've created a million blogs

what a guy

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Will, I'm starting to thing you are on to something with the adding E&M stuff as we go. It will be much easier at the end of the quarter, if we have a good start from adding things on the way. So why don't we use this comment section to write all of the E&M equations and I'll edit the blog every once and a while, and then at the end of the year, repost it so that it will be at the top of the feed and we can all see it

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I'll see if I can't find a way to "Sticky" a link to this post... another you can do is treat it as a "group" blog, where more than one person can write/edit/post to it. I believe you can play with the settings from the top navigation bar where it says "blog settings." I'll do a bit more research, but I know that capability comes with our blogging/messaging software.

Just as an aside, I can't begin to tell you guys how thrilled I am with the effort and thought you're putting in to your posts. Not only are you finding fun and unique physics applications, you're also building tools to help yourselves and the many students who will come after you. Well done!

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