In the realm of kinetic theory of gases, the internal energy of gas is solely due to the sum of kinetic energies of all particles, since kinetic energy is frame dependent I was thinking whether a container having gas will heat up if I put it in a moving train, which is accelerating?
In (non-relativistic) classical physics, if the temperature of an object is proportional to the average kinetic energy ${1 \over 2} m\overline {v^{2}}$of its particles (or molecules), then shouldn't that temperature depend on the frame of reference - since $\overline {v^{2}}$ will be different in different frames?  (I.e. In the lab frame  $K_l = {1 \over 2} m\overline {v^{2}} $, but in a frame moving with velocity $u$ relative to the lab frame, $K_u =  {1 \over 2} m \overline {(v+u)^{2}}$).
Fundamentally, what does a friction force do for a rolling object? I am very confused by the way my textbook explains it. In my textbook , it says:  A wheel rolling on a horizontal flat surface at a constant velocity experiences no friction force. Why?   On the same surface, there is an acceleration of the wheel pointing to the right (probably caused by a force), so the ball is angularly accelerating in the clockwise direction. In this case, a friction force appears, and it is also pointing to the right. How come? What does the friction do for this wheel?  On an inclined plane, a ball freely rolls down the surface. The direction of friction is up the ramp, which confuses me because in the previous example the friction force was in the direction of the wheel's acceleration.   And there is a difference if a wheel is freely rolling and if there is a torque acting on the ball's center of mass. WHY???  What does friction do in these cases? How does it cause an object to roll? Bootstrap CSS Active Navigation Can you ready an action for "immediately before my next turn"? Intuition behind measurable random variables and $\sigma$-algebra I've been trying to understand $\sigma$-algebras and how it encodes information in context of filtration. While certain parts seem clear and logical, I can't say I get the whole picture.  I'll try to explain the counter-intuition I get with the classical example of : the probability space $\Omega = \{ HH, HT, TH, TT \}$ and a r.v. $X(\omega)$ equal to the number of heads.  At times $0$, $1$ and $2$ the available information is represented using $\sigma$-algebras $\mathcal{F}_0=\{\emptyset,\Omega\}$, $\mathcal{F}_1=\{\emptyset, \Omega, \{HH,HT\},\{TH,TT\}\}$ and $\mathcal{F}_2=\{\emptyset, \Omega,\{HH,HT\},\{TH,TT\},\{HH\},\{HT\},\{TH\},\{TT\}\}$.  One can notice that $X(\omega)$ is not measurable with respect to $\mathcal{F}_0$ and $\mathcal{F}_1$, because $X^{-1}((\frac{3}{2}; +\infty))=\{HH\}$. To me it is quite surprising: intuitively $X$ makes perfect sense at all times. In particular it has an expected value at time $0$, which I interpret as that the probability and value of all outcomes $\{\omega\}$ can be computed. How do you think of a non-measurable function?  Here's another way of expressing the same confusion. The most natural choice of $\sigma$-algebra in a finite discrete case is $\mathcal{F}=2^\Omega$, and it is implicitly used in all elementary probability problems. However, this choice of $\mathcal{F}$ does not reflect the fact that some information is known or unknown, conditional probability does. Does it mean that the statement "$\sigma$-algebra is known information" make sense only in conditioning? Why is it convenient then? I'm sure there are many ways to do this: how can I count the number of lines in a text file?  $ &lt;cmd&gt; file.txt 1020 lines Mac OS X Darwin: how to reset admin password? Today I bought an ibook G4 from a garage sale. The people who sold it to me didn't know the password for the 2 accounts on it. Apparently it was the guys late father's laptop. Any suggestions on how to get into the laptop and set a new admin account and password? register_globals error in php I was stuck up with the error   directive 'register_globals' is no longer available in PHP in unknown on line 0   when tried to check the php version using "php -v" after enabling register_globals in php.ini file. I am not getting any php version info by doing so. Instead it throws the above mentioned error.After turning off this option, php info works quite well. It is very essential for me to have register_globals to be turned on.How can I have this corrected.  my php.ini is as follows:   ; Default Value: None ; Development Value: "GP" ; Production Value: "GP" ; http://php.net/request-order request_order = "GP"  ; Whether or not to register the EGPCS variables as global variables.  You may ; want to turn this off if you don't want to clutter your scripts' global scope ; with user data. ; You should do your best to write your scripts so that they do not require ; register_globals to be on;  Using form variables as globals can easily lead ; to possible security problems, if the code is not very well thought of. ;  register_globals = On  ; Determines whether the deprecated long $HTTP_*_VARS type predefined variables ; are registered by PHP or not. As they are deprecated, we obviously don't ; recommend you use them. They are on by default for compatibility reasons but ; they are not recommended on production servers. ; Default Value: On ; Development Value: Off ; Production Value: Off ;  register_long_arrays = Off  ; This directive determines whether PHP registers $argv &amp; $argc each time it ; runs. $argv contains an array of all the arguments passed to PHP when a script ; is invoked. $argc contains an integer representing the number of arguments ; that were passed when the script was invoked. These arrays are extremely ; useful when running scripts from the command line. When this directive is ; enabled, registering these variables consumes CPU cycles and memory each time ; a script is executed. For performance reasons, this feature should be disabled ; on production servers. ; Note: This directive is hardcoded to On for the CLI SAPI ; Default Value: On ; Development Value: Off ; Production Value: Off ; register_argc_argv = Off  ; When enabled, the SERVER and ENV variables are created when they're first ; used (Just In Time) instead of when the script starts. If these variables ; are not used within a script, having this directive on will result in a ; performance gain. The PHP directives register_globals, register_long_arrays, ; and register_argc_argv must be disabled for this directive to have any affect. ; auto_globals_jit = On How to install Wi-Fi driver for Realtek RTL8821CE on Ubuntu 18.04? I'm trying to install drivers for my Wifi on my HP All-in-one desktop. I've been told to show the output of the command "sudo lshw -C network" so here it is:  *-network description: Ethernet interface product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller vendor: Realtek Semiconductor Co., Ltd physical id: 0 bus info: pci@0000:01:00.0 logical name: enp1s0 version: 15 serial: 48:ba:4e:5c:06:5f size: 100Mbit/s capacity: 1Gbit/s width: 64 bits clock: 33MHz capabilities: pm msi pciexpress msix bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168h-2_0.0.2 02/26/15 ip=192.168.1.21 latency=0 link=yes multicast=yes port=MII speed=100Mbit/s resources: ire:31 import:e000(size=256) memory: fea04000-fea04fff memory:fea00000-fea03fff  *-network UNCLAIMED description: Network controller product: Realtek Semiconductor Co., Ltd. vendor: Realtek Semiconductor Co., Ltd. physical id: 0 bus info: pci@0000:02:00.0 version: 00 width: 64 bits clock: 33MHz capabilities: pm msi pciexpress cap_list configuration: latency=0 resources: import:d000(size=256) memory:fe900000-fe90ffff   Output from "lspci -nnk | grep -A2 0280":  02:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821CE 802.11ac PCIe Wireless Network Adapter [10ec:c821] Subsystem: Hewlett-Packard Company RTL8821CE 802.11ac PCIe Wireless Network Adapter [103c:831a] 03:00.0 Unassigned class [ff00]: Realtek Semiconductor Co., Ltd. RTS5229 PCI Express Card Reader [10ec:5229] (rev 01) Need clarification on the Draw 4 rule. - Player 1 lays down a Draw 4 Card and says the color is Red. - Player 2 does not have a Red card but has a Draw 4 Card. Can Player 2 lay down his Draw 4 Card and have Player 3 draw 8 cards? How to copy metadata of Partial Sandbox into a new Developer sandbox? I Have only one license of Partial sandbox. I want to refresh it with Production. Before that I want to copy all the metadata present in the Partial sandbox into New/Existing Developer sandbox. How can do that?  Is it supported by salesforce? or are there any tools available for this requirement.  Thanks. How to typeset the symbol “^” (caret/circumflex/hat) I need to display the symbol '^'  d &lt;- dist(fascores, method = "euclidean")^2   How do I do that? How to sum up values of each two rows across their line in linux I'm trying to change sign text color in Java Edition on Windows 10. According to , this is done using the § symbol:  To enter &quot;§&quot; on Windows with most US/UK English keyboards type ALT + NUMPAD_2 NUMPAD_1  This works for me inside Notepad or this browser. However, when I enter this sequence in the sign input dialog, nothing happens. What could be causing this? Project point onto line in Latitude/Longitude Given line AB made from two Latitude/Longitude co-ordinates, and point C, how can I calculate the position of D, which is C projected onto D.  Diagram: If I do not edit the .bashrc or other config files, the environment variables that I've setted are gone when I logout, or turn off the terminal.   What I'm curious is, where are those 'temporary' env vars saved in?   As I guess, they might be in the memory. That makes sense because they will disappear when the terminal is turned off(equals the terminal I was using is gone from the memory). Am I correct? Given $a + b = 1$, Prove that $a^ab^b + a^bb^a \le 1$; $a$ and $b$ are positive real numbers. It appears that in PHP objects are passed by reference. Even assignment operators do not appear to be creating a copy of the Object.  Here's a simple, contrived proof:  &lt;?php  class A {     public $b; }   function set_b($obj) { $obj-&gt;b = "after"; }  $a = new A(); $a-&gt;b = "before"; $c = $a; //i would especially expect this to create a copy.  set_b($a);  print $a-&gt;b; //i would expect this to show 'before' print $c-&gt;b; //i would ESPECIALLY expect this to show 'before'  ?&gt;   In both print cases I am getting 'after'  So, how do I pass $a to set_b() by value, not by reference? I want to create liveUSB on part of my flash stick. I made a partition with GParted and downloaded .iso file of Ubuntu 19 from the official website to mount with gnome-disk-utility.  I noticed that the iso file has "amd64" in the name. But I intend to use this USB not only on amd computers!  Is that important? Will the live USB work on PC with Intel/other processor? Edit Mail rules manually How can I manage the "Open with Explorer" button based on user permissions?