I thought the center of mass equation was derived for general forces, $$\sum{\vec{F_{ext}}}=M\vec{a_{CM}}$$  Then suddenly when the external force on the $i$ particle is of the form $m_ig_i$, where $g_i$ varies throughout the body, we have to use this equation:  $$\vec{W}=M\vec{a_{CG}}$$  where $CG$ is a different point than $CM$. So, what makes gravity special?  EDIT: I'm not asking the difference between them. They have different formulas, so obviously they have different values when $g$ is not constant.  I'm asking why doesn't the resultant gravitational force or $W$ can't be thought of as acting on the center of mass when the center of mass equation is derived for any general external force.
My book says:     For most of the small objects, both are same. But for mammoth ones, they are really different ones. And in a gravity-less environment, COG is absent; COM still exists.   Ok, what's the big deal when things are small and big? How these two :  &amp; ?
My brother owns Skyrim on steam. We use Steam Family Share, but we were wondering how both of us could play it at the same time? I changed my hostname, why is my bash PS1 prompt unchanged? Is there a term for an issue or activity that occurs only until the moment that you ask someone else to watch? Is there a term for the coincidence that occurs when an issue ONLY occurs until the moment that you ask someone else to watch or help you resolve it?    For example, having an issue with software until you try to show someone, then it stops being problematic.  Or an issue with the computer/phone that resolves as soon as a help ticket is put in.    The final example is when you have a problem with your car (funny noise, etc) - you hesitate taking it in for weeks because you know it will disappear as soon as the mechanic drives it...then it does.    This is different than a , where the action of applying a debugger, for example, changes the behavior of the activity being watched.  It's also different from a 'works on my machine' scenario, where only the original user has the problem.   What is it called when a problem resolves itself just by the mention of it?  Jinxing the issue? :)  I see this every day supporting my software product -- the users are experienced and are not making mistakes at one time then doing something different when I watch.  The problems also truly resolve (coincidentally) as soon as they ask for help - they do not reoccur.  I guess it's a case of synchronicity? Deleting comments and review actions cause layout to be broken, AJAX response contains full page Java is one of my programming languages of choice.  I always run into the problem though of distributing my application to end-users.  Giving a user a JAR is not always as user friendly as I would like and using Java WebStart requires that I maintain a web server.  What's the best way to distribute a Java application?  What if the Java application needs to install artifacts to the user's computer?  Are there any good Java installation/packaging systems out there? Could we send a man safely to the Moon in a rocket without knowledge of general relativity? Printing an SE page in Firefox shows only the first page I used to print Q&amp;A pages to keep a base of PDFs. I used either the 'print edit' addon or simply the print function of Firefox, which both allow to print a webpage in a file.  Usually the printed file for a webpage extends on 2 or 3 pages. But I'm not able to print more than one page on this site expressly anymore. No matter the method. I just get the top of each discussion. How can I have  for Ubuntu? 11.4 Full Jaillbreak method Yet? I've been searching around for a a while now and So far I haven't found any full jailbreaks for ios 11.4 on a 6s. To be honest, I am new to the jailbreaking scene. I've installed Velonzy, but could find no jailbreaking tools. Am I missing something, or is there truly nothing left.  PS. I would downgrade to a system-rootable version but I haven't any SHSH blobs, or found any alternative method. Is it possible? using a:hover to change the color of an image If $f$ is a continuous function with $\displaystyle \int_{0}^{x}f(t)dt\rightarrow \infty$ as $|x|\rightarrow \infty\;,$ Then show that every line $y=mx$ Intersect the curve $\displaystyle y^2+\int_{0}^{x}f(t)dt=2$  $\bf{My\; Try::}$ Put $y=mx$ in $$\displaystyle y^2+\int_{0}^{x}f(t)dt=2\;,$$ We get $$\displaystyle m^2x^2+y^2+\int_{0}^{x}f(t)dt=2.$$ We can write it as $$\displaystyle 2\int_{0}^{x}2m^2tdt+\int_{0}^{x}f(t)dt=2$$ So $$\displaystyle \int_{0}^{x}\left[2m^2t+f(t)\right]dt-2 =0$$ Now Let $$g(x) = \displaystyle \int_{0}^{x}\left[2m^2t+f(t)\right]dt-2.\;,$$ When $x\rightarrow \infty\;,$ Then $g(x)\rightarrow \infty.$ (Where $g(x)$ is an Continuous function.) Now I did not Understand How can i solve that, Help me Thanks Book, it follows a guy in a dystopian future I was wanting to initialize some strings at the top of my script with variables that have no yet been set, such as:  str1='I went to ${PLACE} and saw ${EVENT}' str2='If you do ${ACTION} you will ${RESULT}'   and then later on PLACE, EVENT, ACTION, and RESULT will be set. I want to then be able to print my strings out with the variables expanded. Is my only option eval? This seems to work:  eval "echo ${str1}"   is this standard? is there a better way to do this? It would be nice to not run eval considering the variables could be anything. Is there a single word for "one who speaks/boasts a lot about everything"? I'm looking for a single word to most aptly describe a person possessing the following "qualities":   Appears to be superior in every technology/skill under the sun, which he deems worthy of knowing On being questioned/assigned the task, is found to have only superficial/no knowledge of the said skill. Inherent tendency to "one-up" anyone and everyone - example: "I didn't work hard at all in my undergrad days, but yet I have better/equal grades than you have! "   Could someone help?  Edit: I've got some very good responses, but despite popular opinion for "braggart", I'm going with "pretentious" as it suits what I was looking for more aptly IMHO. Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$ Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$?  The correct answer should be 4. Scanner is skipping nextLine() after using next() or nextFoo()? Is there the easiest way to toggle (show/hide) navigational grids in TikZ? In PSTricks, we can toggle the grids easily by showgrid=[false/true]. How to do it in TikZ? Doing as follows is tedious.    \documentclass{minimal} \usepackage{tikz}  \begin{document}   \tikzpicture  \draw[gray,very thin] (-4,-2) grid (4,2); \foreach \x in {-4,...,4}   \draw[red] (\x,-1.9) -- (\x,-2.1) node [below] {\x};   \foreach \y in {-2,...,2}   \draw[red] (-3.9,\y) -- (-4.1,\y) node [right] {\y};  \draw (0,0) circle (2);   \endtikzpicture    \end{document}   Is there the easiest way to toggle (show/hide) navigational grids in TikZ?  Edit  The navigation needs not only the grids but also the labeling numbers. Is there any way to check whether a file is locked without using a try/catch block?    Right now, the only way I know of is to just open the file and catch any System.IO.IOException. Contraction Map on Compact Normed Space has a Fixed Point So I know umask can restrict privileged users, using this format umask ugo.  I understand that the read = 4, write = 2, and exec = 1. However, when I type umask, it returns 4 digits which is 0022 or 0073. I have no understanding of how does this work now because there is an extra digit. What is that extra digit and what does 0022 mean?