I am almost a little embarrassed to be asking this question since my education and experience is in mechanical engineering.  However, I've drawn a few diagrams, but am still a little puzzled by this question...  In my diagrams, the vectors I've drawn don't seem to actually produce a resultant force that would actually push the vehicle one way or the other when a turn is desired....    From everyday experience, the short answer is that the actual forces that cause a vehicle to turn are due to frictional forces.  Anyone that has driven a car on reduced traction roads due to slush and ice can attest that those conditions result in a car usually not wanting to turn in the direction the steering wheels are turned.  Furthermore it isn't hard to imagine a car already in motion on a totally frictionless surface - turning the front wheels one way or the other would not make the vehicle turn in that direction at all...  For this case, please only consider a car with rear wheel drive and front wheel steering.  It seems rather obvious that in vehicle configurations where the steering wheels are also driving wheels (that is, front wheel drive, AWD, or 4WD), then the vehicle turns in the direction the steering wheels are turned because the actual forces the road surface exerts on the wheels are turned relative to the centerline and CG of the vehicle.  In a car with front steering and rear driving wheels, every part of the car forward of the rear driving wheels is being pushed forward by the rear driving wheels.  The car wants to go in a straight line.    Imagine that the car is in motion going forward and that the front wheels are turned only very slightly to left or right (a few degrees left or right of directly straight ahead), what force vectors and resultant actually produce the 'kick' that causes the entire front end of the vehicle to turn in the desired direction?  It is obvious that a rolling tire wants to continue rolling and that turning the wheel relative to its initial straight-ahead path would produce a scuffing situation - a high friction situation compared to rolling.    In a related situation, we can examine when a car is not in motion, but stopped. When a vehicle is at a complete stop and the front wheels are turned in the direction of an intended turn and obviously not rolling in the forward direction, what are the force vectors that result in the front of the vehicle turning in the direction of intended motion?  In my diagrams, I've isolated and examined the forces on the steering tires' contact patch with the road, but still cannot resolve a frictional force vector that would explain why the front end of the car turns...  I've even considered the gyroscopic effect of rotating wheels and thought that it might be due to a force that is exerted on a rotating wheel that has its rotating axis deflected when the wheels are steered - again I wasn't able to find anything and the gyroscopic restoring force would not explain how a stationary turned wheel causes a vehicle to turn anyway...  Please help me understand this seemingly simple concept....
When a ball moves to the right, friction acts to oppose the motion, in other words, to the left. However, when a car travels around a bend, the friction acts in the perpendicular direction to the car's velocity and provides the centripetal force. I just cannot understand why friction would act in that direction.
How can i make my Java Swing GUI Components [Right To Left] for Arabic language from NetBeans Desktop Application? I love R. Courant and F. John's Introduction to Calculus and Analysis because of its wide coverage, precise description and friendly written style.  Are there any classic textbooks like it on ODE/PDE?  thanks. For some reason, be it some bad habit or something else, I can not understand why the statement "p only if q" would translate into p implies q. For instance, I have the statement "Samir will attend the party only if Kanti will be there." The way I interpret this is, "It is true that Samir will attend the party only if it is true that Kanti will be at the party;" which, in my mind, becomes "If Kanti will be at the party, then Samir will be there."   Can someone convince me of the right way?  EDIT:  I have read them carefully, and probably have done so for over a year. I understand what sufficient conditions and necessary conditions are. I understand the conditional relationship in almost all of its forms, except the form "q only if p." What I do not understand is, why is p the necessary condition and q the sufficient condition. I am not asking, what are the sufficient and necessary conditions, rather, I am asking why. Getting a standard form quadratic from a set of points ($3$ points) I came home from school today, pulled out my homework, now I'm stumped.  I don't want the answer, I just want to know how to do it.  Here is the question that I'm reading:  Determine a quadratic function in standard form for the set of points $(x_1,y_2)(x_2,y_2)(x_3,y_3)$  Where the $x$'s and $y$'s represent the points.  Here are the points I am working with (remember, I don't want the answer, I just want to know how to do it, there are lots of questions on this so I want to be able to know how to do it).     $(-1, 2), (0, 1), (1, -4)$   Thanks! Scamming a scammer? I have seen many questions like:      My question is: what happens if you receive this money (without doing anything or giving your bank account number) but do not do anything scammer wants?  I especially want to know about what happens with the money you got and possible legal consequences.    Is it considered yours because scammer transfered it to you? Do you have to return it? If yes, to whom and in what form? And finally, how is it that scammers are just sending money to random people? Aren't they scared that someone will simply not return it? I understand that this may be stolen money, but it surely took some effort (cash/time) to "acquire" it, so why are they just sending it away? "At least one" - singular or plural subject? Starting multiple Chrome full screen instances on multiple monitors from (batch) script My goal is to show different web content full screen on multiple monitors automatically after booting from a single computer. The browser I would like to use is Chrome. If Chrome does not support this and Firefox does that would be fine.  The OS I would prefer is Windows, if it turns out that Linux is possible that would be fine.  On Windows it is possible to set the position of the Chrome browser window (--window-position=) and make Chrome start in full screen mode (--kiosk). Using these options combined you can start Chrome full screen on any of the desktops/screens that you have connected to your computer. I have managed to get this working.  However, if I then try to do the same thing a second time to have Chrome full screen on a second screen the second Chrome window will open over the first window, no matter the coordinates I use for the --window-position parameter.  I have tried using Chrome profiles and copying the Chrome directory and starting the second chrome.exe. All these things result in the same behaviour. Old title - "change resolution to 1280x1024 using xrandr gives: X Error of failed request: BadValue (integer parameter out of range for operation)"  I have installed a fresh Ubuntu 17.10 and have a monitor with 5:4 resolution. settings has no resolution higher than 1024x768. But I need the resolution 1280x1024 (5:4).  I use the default motherboard graphics card:  # lspci|grep VGA 00:02.0 VGA compatible controller: Intel Corporation 4 Series Chipset Integrated Graphics Controller (rev 03)   Also xrandr gives the following:  $ xrandr Screen 0: minimum 320 x 200, current 1024 x 768, maximum 8192 x 8192 XWAYLAND0 connected 1024x768+0+0 (normal left inverted right x axis y axis) 0mm x 0mm    1024x768      59.92*+   I tried to add the 1280x1024 resolution using xrandr. so first created the resolution information using gtf:  $ gtf 1280 1024 60    # 1280x1024 @ 60.00 Hz (GTF) hsync: 63.60 kHz; pclk: 108.88 MHz   Modeline "1280x1024_60.00"  108.88  1280 1360 1496 1712  1024 1025 1028 1060  -HSync +Vsync   Then added to resolutions:  xrandr --newmode "1280x1024_60.00"  108.88  1280 1360 1496 1712  1024 1025 1028 1060  -HSync +Vsync   then again did the command: xrandr --addmode XWAYLAND0 1280x1024_60.00  Then nothing changed. When I tried to change it using xrandr --output XWAYLAND0 --mode 1280x1024_60.00 --rate 60 But an error occurred:  $ xrandr --output XWAYLAND0 --mode 1280x1024  --rate 60 X Error of failed request:  BadValue (integer parameter out of range for operation)   Major opcode of failed request:  140 (RANDR)   Minor opcode of failed request:  7 (RRSetScreenSize)   Value in failed request:  0x0   Serial number of failed request:  21   Current serial number in output stream:  22   I don't know what did I do wrong. Or how to change resolution to the correct one: 1280x1024 How to iterate over arguments in a Bash script The following MWE compiles (for me)  \documentclass{article}  \usepackage{pgfplots} \pgfplotsset{compat=newest} \usetikzlibrary{external} \tikzexternalize[prefix=figures/externalized/]   \begin{document} \begin{figure}     \centering     \begin{tikzpicture}          \begin{axis}  %           \addplot3[surf,mesh/rows=129,mesh/cols=129,mesh/ordering=y varies] table[x=X,y=Y,z=psi] {figures/data/LidDrivenCavity/Lid_SPIKE_128x128_Re1000_psi.dat};              \addplot3[contour gnuplot,mesh/rows=129,mesh/cols=129,mesh/ordering=y varies] table[x=X,y=Y,z=psi] {figures/data/LidDrivenCavity/Lid_SPIKE_128x128_Re1000_psi.dat};          \end{axis}      \end{tikzpicture}     \caption{ciao} \end{figure} \end{document}   where the data file is . If I de-comment the first \addplot3 and comment the second one, then I get an error. The final part of the log file (the interesting one, I think) is  ===== 'mode=convert with system call': Invoking 'pdflatex -shell-escape -halt-o n-error -interaction=batchmode -jobname "figures/externalized/prova-figure0" "\ def\tikzexternalrealjob{prova}\input{prova}"' ======== \openout3 = `prova.auxlock'.  runsystem(pdflatex -shell-escape -halt-on-error -interaction=batchmode -jobname  "figures/externalized/prova-figure0" "\def\tikzexternalrealjob{prova}\input{pr ova}")...executed.  \openout3 = `prova.auxlock'.   ./prova.tex:22: Package tikz Error: Sorry, the system call 'pdflatex -shell-esc ape -halt-on-error -interaction=batchmode -jobname "figures/externalized/prova- figure0" "\def\tikzexternalrealjob{prova}\input{prova}"' did NOT result in a us able output file 'figures/externalized/prova-figure0' (expected one of .pdf:.jp g:.jpeg:.png:). Please verify that you have enabled system calls. For pdflatex,  this is 'pdflatex -shell-escape'. Sometimes it is also named 'write 18' or som ething like that. Or maybe the command simply failed? Error messages can be fou nd in 'figures/externalized/prova-figure0.log'. If you continue now, I'll try t o typeset the picture.  See the tikz package documentation for explanation. Type  H &lt;return&gt;  for immediate help.  ...                                                l.22    \end{tikzpicture}  ?  PGFPlots: reading {figures/data/LidDrivenCavity/Lid_SPIKE_128x128_Re1000_psi.da t} Runaway argument? {\pgfkeyssetvalue {/pgfplots/execute at begin plot visualization}{}\pgfkeyssetv alue \ETC. ./prova.tex:22: TeX capacity exceeded, sorry [main memory size=5000000]. &lt;argument&gt; ...5e-1],2Y7.753628e-3]}{2Y8.20894\ETC.  l.22    \end{tikzpicture}  If you really absolutely need more capacity, you can ask a wizard to enlarge me.   Here is how much of TeX's memory you used:  20761 strings out of 493054  547383 string characters out of 6134761  5000001 words of memory out of 5000000  23958 multiletter control sequences out of 15000+600000  3640 words of font info for 14 fonts, out of 8000000 for 9000  1141 hyphenation exceptions out of 8191  62i,4n,84p,728b,1519s stack positions out of 5000i,500n,10000p,200000b,80000s ./prova.tex:22:  ==&gt; Fatal error occurred, no output PDF file produced!   similar (or the same) error appears if externalization is not enabled/used.  My TeX distribution is TeX Live on Mac OS X 10.9.5 and I use TeXShop as editor.  Once I (partially) solved a  on Windows+MikTeX+TeXniccenter by modifying/adding options to the command executed when compile button is pressed. I say partially since I actually solved the problem for some data file. Then I experienced the same problem with larger datafile and/or different plots (I don't remember anymore) and didn't find a way out, no matter how much I extended the memory.  What should I do now? Irreducible conics An algebraic set (not necessairly a variety) $X \subseteq \mathbb{A}^2$ defined by a polynomial of degree $2$ is called a conic.  The problem is:     Show that any irreducible conic is isomorphic either to $Z(y-x^2)$ or to $Z(xy-1)$ after an affine change of coordinates in $\mathbb{A}^2$.   However, with this definition of conic, I only can conclude that if the polynomial is irreducible, then the conic is irreducible (because $f$ irreducible $\Rightarrow Z(f)=X$ is irreducible)     What can I do to prove that if a conic is irreducible, then the polynomial that defines the conic is irreducible?   And for the main problem, how can I do the affine change of coordinates?  Thanks What's the most efficient way of determine individual card values for my collection? Was it just coincidence that Tahir Mahmood went on stage? Difference between "not equal" operators  and != in PHP Is it possible to extend an Indian business visa from India? I'm an Egyptian girl from Cairo. I'm planning a six-month trip to India in December for training purposes, but getting a six-month visa is so hard from my country.  If I can only get 3 months instead of 6 months, is it possible to extend the business visa in India? How to parse a query string into a NameValueCollection in .NET I would like to parse a string such as p1=6&amp;p2=7&amp;p3=8 into a NameValueCollection.  What is the most elegant way of doing this when you don't have access to the Page.Request object? Windows Starter Edition, Home and Home Premium do not include gpedit, how do I install it? I want to make some changes to Windows that require using the Group Policy Editor (gpedit.msc).  Unfortunately the Group Policy Editor is not included with the Starter Edition, Home and Home Premium editions of Windows.  How can I install it? How do I completely uninstall Google Chrome and Chromium? I'm having a problem with Chrome and one of its extensions, so I want to completely uninstall everything. I've uninstalled Chrome through the Software Center, but when I reinstall it, all of my extensions and preferences are still there.   If I want to start over from scratch, what do I need to do? Update help center on syntax highlighting to point to an actual list of options Reading the help center article on syntax highlighting, one of the paragraphs within it reads:     You can use either , like lang-cpp or lang-sql, or you can specify a tag, and the syntax highlighting language associated with this tag will be used:   Note the link in there, which goes to .  Problem is, a long time ago we removed the list of options from several questions/answers across meta Stack Exchange because it was a pain trying to keep all of them updated. It makes a lot more sense to just have one list that we keep updated, and the most logical place for that list was in the , which is where it now resides.  Can the link in the help center be updated to point directly to the list, rather than to a post that explains that the list has been moved? Compute: $\lim_{x\to 0}\frac{\sqrt[m]{\cos(\alpha x)}-\sqrt[n]{\cos{(\beta x)}}}{x^2},\;m,n\in\mathbb N,\alpha,\beta\in\mathbb R$ Compute: $$\lim_{x\to 0}\frac{\sqrt[m]{\cos(\alpha  x)}-\sqrt[n]{\cos{(\beta x)}}}{x^2},\;m,n\in\mathbb N,\alpha,\beta\in\mathbb R$$   My attempt:  $$L=\lim_{x\to 0}\frac{\sqrt[m]{\cos(\alpha x)}-\sqrt[n]{\cos{(\beta x)}}}{x^2}=\lim_{x\to 0}\frac{\sqrt[m]{\cos(\alpha x)}-1+1-\sqrt[n]{\cos(\beta x)}}{x^2}\\\displaystyle=\lim_{x\to 0}\frac{\left(1+(\cos(\alpha x)-1)\right)^{\frac{1}{m}}-1-\left(\left(1+(\cos(\beta x)-1)\right)^{\frac{1}{n}}-1\right)}{x^2}$$  Transformed expression: $$-\frac{(1+(\cos(\alpha x)-1))^{\frac{1}{m}}-1}{\cos(\alpha x)-1}\cdot\frac{1-\cos(\alpha x)}{\alpha^2x^2}\alpha^2+\frac{(1+(\cos(\beta x)-1))^{\frac{1}{n}}-1}{\cos(\beta x)-1}\cdot\frac{1-\cos(\beta x)}{\beta^2x^2}\beta^2$$  I applied the standard limits from the table: $$\lim_{x\to 0}\frac{(1+x)^a-1}{x}=a\;\&amp;\;\lim_{x\to 0}\frac{1-\cos x}{x^2}=\frac{1}{2}$$ $$L=-\frac{1}{m}\cdot\frac{1}{2}\alpha^2+\frac{1}{n}\cdot\frac{1}{2}\beta^2=\frac{m\beta^2-n\alpha^2}{2mn}$$ Is this correct?