I have a query which I cannot resolve by finding enough arguments. A perfectly round wheel that also doesn't have any contractions due to gravity is placed in a perfect vacuum, so no drag is present. Will it stop due to friction force or will it roll forever?
I have already read        and many others   But I still have the following problem:   On one hand I've been told that if pure rotation takes place then the object goes on forever. This must imply no frictional force in any form acting on the body. On the second hand I've been told that during pure rotation(no external forces like wind) on a plane surface friction acts opposite to velocity of center of mass (accompanied by change of normal) and slows it down.     Both seem logical enough: The point of contact doesn't slip therefore no friction is required; So no retarding force and it must go on. Things don't go on forever; Friction must be present to slow it down.    So, which hand is correct? Or is there a third hand altogether?
Why do we use the object instead of the subject pronoun in constructions like "stupid me"? I'm trying to find out how come we say lucky me and stupid us rather than lucky I and stupid we. My understanding is that this is not a recent invention, but a relic from the distant past where it was a dative construction. However, I don't see the reason for using any case other than the nominative in this construction to begin with.        He went surfing. → Lucky him went surfing.   I got pulled over. → Stupid me got pulled over.   They bought a house. → Thoughtless them bought a house.      This is rather intriguing. After thinking about it for a while, I couldn't come up with any other language, Germanic or otherwise, where simply introducing an adjective would dictate a change of grammatical case. This appears to be an English peculiarity. How far can it be traced back? Can anyone comment on its background? How to enable automatic update in wordpress running on IIS7 and Windows 2008? I have a dedicated server using Windows 2008 and IIS7 running 5 blogs with Wordpress. I can't use the autoupdate feature of the wordpress neither the automatic plugin instalation.  I believe I must set writing permissions in some temporary folder, the question is which one. Do you have any idea? How to sort two lists (which reference each other) in the exact same way From time to time, I need to typeset Welsh. Sometimes, I need to typeset citations and bibliographies in Welsh. I think that last time I did this, I may still have been using BibTeX although I am honestly not sure. In any case, my entire work-flow now uses biber and biblatex...  I found  on changing the names of things, including the names of things used by biblatex. However, that cannot deal with the case of an unsupported language.  Suppose that I want to typeset a document in Welsh:  \documentclass[a4paper,welsh]{article}  \usepackage{babel} \usepackage[utf8]{inputenc}% welsh needs utf8x but biblatex doesn't like it \usepackage[T1]{fontenc}% not great for Welsh but the best pdfTeX can do \usepackage{csquotes}% doesn't like Welsh though biblatex likes csquotes on account of babel... \usepackage[backend=biber]{biblatex} \bibliography{biblatex-examples}  \title{Fy Nogfen} \author{Rhywun}  \begin{document}   \maketitle   \tableofcontents   \section{Cyntaf}   \autocite{westfahl:space}    \printbibliography  \end{document}   There are multiple problems in such a case. (One is that I need utf8x but can't use it on account of biblatex. Another is that I need utf8x at all. Another is that biblatex likes csquotes but csquotes doesn't do Welsh. But these are irrelevant to this question.)  The output is as follows:    Note that the use of the English citation is just so this is easy to reproduce. Obviously, the content of the reference might well be in Welsh. (Though it might be in English, too.)  As can be seen, while elements of the document controlled by babel are handled correctly, those under the control of biblatex are not. However, I cannot simply modify the solution offered by lockstep for changing strings to customised English variants. That is, I can't just use a Welsh version of  \DefineBibliographyStrings{english}{%   bibliography = {Works Cited},   references = {Works Cited}, }   because biblatex has never heard of it.  What is the most appropriate way to configure biblatex for use with an unsupported language? Change this behavior to allow for spelling corrections and the like: "Edits must be at least 6 characters" Now, it is easy to workaround this: add 10 characters, plus your one-character change, then remove these 10 characters in the next edit for the same post.  But this can hardly be what the designers intended. Instead, my suggestion is to change it to something like on Wikipedia, where you can mark an edit as "minor". Something like this:     Edits must be at least 6 characters, or select the checkbox "Minor, spelling or punctuational correction."   Edits like that will, of course, not count toward the edit-limit (before it becomes Community Wiki).  The suggestion often seen on Meta Stack Overflow is "just edit more in that post". But sometimes the post is just right, and there aren't any other spelling mistakes to correct. Why force a user to change more than necessary, or use an ugly hack? I'm using Ubuntu 17.10 with GNOME shell and Numix-Circle icon theme.   When I hover over the Numix icon for Nightly Web Browser, which is pinned to the dock I get the title "Nightly Web Browser".      But when I launch the program, another icon pops up at the bottom, with the name "Nightly". Cannot select text in Safari address bar Clicking links in pdfs opened with Okular opens Abiword (instead of the default browser) I work with Xubuntu 12.04 and use Okular (version 0.14.3) to view pdf files. If I click a web link in a pdf file (created with "pdflatex" using the "hyperref" package), "Abiword" (It's a word-processing software, like Libreoffice writer) is opened instead of my default browser google-chrome. How can I change this behavior? The settings in Okular do not seem to provide a solution.   (Note that I set google-chrome as the preferred application for web browsing under Settings -> Preferred Applications, so that's not the problem). How to attach CGPDFDocument/CGPDFPage to MFMailComposeViewController Can I use a card with "Add one mana of any color to your mana pool" in any Elder Dragon Highlander (EDH) deck? I recently tried /, and found it to be a ton of fun.  I've started customizing one of the pre-cons I got, but I'm a little confused by some of the deck-building requirements.  According to the deck-building rules:   A card's color identity is its color plus the color of any mana symbols in the card's rules text. A card's color identity is established before the game begins, and cannot be changed by game effects. Cards in a deck may not have any colors in their identity which are not shared with the commander of the deck. (The identity of each card in the deck must be a subset of the General's)    If I'm using  as my general, my deck's identity is Red, Blue and Green.  I couldn't use  in my deck, because it has a black mana symbol in the rules text.  My question is:  can I add a card to my deck that has the phrase "Add one mana of any color to your mana pool" (such as  or )?  Even though those cards could conceivably add black mana to my mana pool, they don't have a black or white (or any for that matter) mana symbol in their rules text, so they would be valid for inclusion in any deck? Is $2^\sqrt{2}$ irrational? Is it transcendental? How to find normal and lognormal moments, given partial information? $Y=\ln(X)$. $X$ is lognormal and $Y$ is normal. If all I know is the arithmetic mean of $Y$ and the standard deviation of $X$. What is the formula to calculate the arithmetic mean of $X$ and the standard deviation of $Y$? How to extrude and scale with an even offset? I have an executable program (no source code, just the compiled executable) that was made in windows (.exe extension).  It doesn't use any graphics... it simply reads and writes files.  I want to be able to run it in a linux shell script so that I don't have to switch operating systems to get my output.  Is there a way to use or convert the executable for linux operating systems? Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle? We have two theorems about Cartesian product:   A finite Cartesian product of countable sets is countable; A countable infinite Cartesian product of countable sets is not necessarily countable.   To prove the first theorem, we can show   Firstly, we can prove $A\times B$ is countable,  Secondly, suppose it is true for $n-1$, i.e. $X=A_1\times A_2\times \ldots \times A_{n-1}$ is countable, we prove the case for $n$ by the fact $A_1\times A_2\times \ldots \times A_{n-1}\times A_{n}=X\times A_{n}$ is in fact the product of two countable sets, in above we know it is still countable.   The above method to prove the first theorem is exactly the mathematical induction, which should show the theorem is true for all $n\in\mathbb{Z}_{+}$, so it should works for countable infinite unions.  However, we may use Cantor diagonal method to prove at least $\{0,1\}^w$ is not countable, thus the second theorem is also right. Does this means that the mathematical induction is wrong?    EDIT: After the following discussions, I have the answer:  The key point is that any element $n\in\mathbb{Z}_+$ is always a finite number, thus induction principle only guarantee the theorem is true for any $n\in\mathbb{Z}_+$, i.e. for any finite number.  When discuss a countable infinite union, it is infinite number of unions, this infinite number no more belong to $\mathbb{Z}_+$, thus can not be guaranteed by induction principle. How to see time stamps in bash history? Is there any way I can see at what time the commands were executed from the bash history? We can see the order but is there any way I can get the time also?  Bottom-Line: Execution time in the Bash history Brand new laptop, two years in storage, will the battery be ok? I have an opportunity to buy a brand new (sealed box) EliteBook 8470p laptop for a good price.  The date of manufacture goes back to around March 2013, which is bang on two years ago.  Given that it's been two years, what state will the supplied Lithium-Ion battery be in? Still usable? The question is to calculate the radius of convergence of $\sum\limits_{n=0}^\infty n!x^{n^2}$.  I dont know how to calculate R.O.C for such type of questions involving $n^2$ as power of x. How do we do this? Any help appreciated. tikz: Distribute evenly and randomly circles I want to fill a part of a picture with more or less evenly and randomly distributed circles which should not overlap. It would be okay if circles are only partly inside the shape.  The density should be like what you see on this page  with values 80-100. (But I do not need so many circles, 30 should be enough, I could repeat the pattern).   I cannot use a grid and "wobble" the circles a bit: The circles are too large and it simply does not look randomly.   Currently I am thinking about a random attempt: Get some random point, measure its distance to existing circles, either paint or throw the point away. Try 100 times and hope that you get the right number of circles (and that it does not take too long). But perhaps someone has a better idea.   The example draws the circles simply manually:  \documentclass{article} \usepackage{tikz} \usetikzlibrary{backgrounds} \begin{document}   \begin{tikzpicture}[framed,gridded,radius=0.5cm]  \draw[red](0,0) rectangle (5,5);   \draw (1,1) circle;   \draw (2.3,1.1) circle ;   \draw (4.5,0.8) circle ;   \draw (5.1,1.8) circle ;   \draw (0.4,3.3) circle ;   \draw (2.1,2.8) circle ;   \draw (3.8,3.5) circle ;   \draw (4.8,4.2) circle ;   \draw (0.8,4.9) circle ;   \draw (2.1,4.1) circle ;   \draw (3.8,2.0) circle ;   \draw (3.5,0.6) circle ;   \draw (3.0,5.0) circle ;      \draw (4.1,5.1) circle ;             \draw (0.9,2.1) circle ;  \end{tikzpicture}  \end{document} Why cant I navigate to lightning component in communities? Im on a lightning community, i have a lightning component and i want to open another component with this code:  navigateToMyComponent : function(component, event, helper) {     console.log('1');     var evt = $A.get("e.force:navigateToComponent");     console.log('2');     evt.setParams({         componentDef : "c:CompetenciaComponent"     });     console.log('3');     evt.fire();     console.log('4'); }   this its the console log:   NOTHINGS HAPPEND AND I DONT KNOW WHY