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I have been told [Warning: I leave this because it's what I asked and allows to understand the dialogues in the comments, but Azad, whom I thank, has pointed that the formula does not hold in general in the form it is expressed] that the angular momentum of and rigid body with respect to any point $P$ can always be expressed as $$\mathbf{L}_{P}=\mathbf{r}_{cm}\times M\mathbf{v}_{cm}+\big(\sum_im_iR_i^2\big)\boldsymbol{\omega}$$ where $\mathbf{r}_{cm}$ is the position of the centre of mass with respect to $P$, $M$ the mass of the body, $R_i$ the distance of the $i$-th point, having mass $m_i$, composing the body, and $\sum_im_iR_i^2=I$ its moment of inertia with respect to the instantaneous axis of the rotation around the centre of mass of angular velocity $\boldsymbol{\omega}$.  I know that the velocity $\mathbf{v}_i$ of each point $P_i$, having mass $m_i$, of a rigid body of mass $M$ can be see as the sum of a translation velocity of one of its points $C$ plus a rotation velocity around that point: $\mathbf{v}_i=\mathbf{v}_{C}+\boldsymbol{\omega}\times\overrightarrow{CP_i}$. If we chose $C$ as the centre of mass I see that $$\mathbf{L}_{cm}=\sum_i \overrightarrow{CP_i}\times m_i\mathbf{v}_{i}=\sum_i \overrightarrow{CP_i}\times m_i\mathbf{v}_{cm}+\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i})$$$$=\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i}) $$because, if I am not wrong, $\sum_i \overrightarrow{CP_i}\times m_i\mathbf{v}_C=(\sum_i m_i\overrightarrow{CP_i})\times\mathbf{v}_C=\mathbf{0}$ since $\sum_i m_i\overrightarrow{CP_i}$ is the position of the centre of mass with respect to itself, which is $\mathbf{0}$.  How can it be proved that $\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i})=(\sum_im_iR_i^2)\boldsymbol{\omega}$? I have searched a lot on the Internet and on books, but I find nothing. To give some background of mine, I have studied nothing of analytical mechanics. I find the formula very, very interesting both in itself and because, if the moment of inertia does not depend upon time, $\forall t\quad I(t)= I(t_0)$, the above expression can be differentiated to get the formula of the resultant torque with respect to the centre of mass $\sum\boldsymbol{\tau}_{cm}=\frac{d\mathbf{L}_{cm}}{dt}=I\boldsymbol{\alpha}_{cm}$ where $\boldsymbol{\alpha}$ is the angular acceleration around the centre of mass. I heartily thank you for any answer!    Some unfruitful trials: by using the "BAC CAB identity" as suggested by Azad, whom I heartily thank, $\mathbf{a}\times(\mathbf{b}\times\mathbf{c})=(\mathbf{a}\cdot\mathbf{c})\mathbf{b}-(\mathbf{a}\cdot\mathbf{b})\mathbf{c}$, I can see that$$\sum_i \overrightarrow{CP_i}\times m_i(\boldsymbol{\omega}\times\overrightarrow{CP_i})=\sum_im_i\|\overrightarrow{CP_i}\|^2\boldsymbol{\omega}-m_i(\overrightarrow{CP_i}\cdot\boldsymbol{\omega})\overrightarrow{CP_i}$$which, by decomposing every $\overrightarrow{CP_i}$ into an axial component $\mathbf{A}_i$ and a radial component $\mathbf{R}_i$, whose norms respectively are $A_i$ and $R_i$, with $R_i$ as the distance from $i$ to the axis of rotation, becomes $$\sum_im_iR_i^2\boldsymbol{\omega}+\sum_i m_i A_i^2\boldsymbol{\omega}-m_i(\mathbf{A}_i\cdot\boldsymbol{\omega})\overrightarrow{CP_i}$$but I cannot prove that $\sum_i m_i A_i^2\boldsymbol{\omega}-m_i(\mathbf{A}_i\cdot\boldsymbol{\omega})\overrightarrow{CP_i}=\mathbf{0}$. Command for creating a directory and navigating into it directly? Lowering elevation of lake using QGIS I am in QGIS. I have a raster layer of mountains and a lake. I have a vector layer (shapefile) of the lake. It sits nicely where it supposed to be over the raster level. I am going to convert this height map to an STL so that I can cnc this out of wood, so I'd like the actual lake to be something like 200 feet lower than it shows on the raster layer so that I can fill it with blue epoxy. I have read a lot of clipping and everything else, and I am lost. Opening a context menu (with the Menu key) I can't solve this problem:  Suppose $f$ is polynomial function of even degree $n$ with always $f\geq0$.  Prove that $f+f'+f''+\cdots+f^{(n)}\geq 0$. Why cannot fermions have non-zero vacuum expectation value? How to skip validation when a specific button is clicked? Why does Google not consider dot in usernames of Gmail addresses? How do I check if a list is empty? When is it kosher to delete one's own answer? According to , the only restriction on self-deleting an answer is that you can't delete an answer that's been accepted.  But I've also heard of users getting in trouble for deleting (non-accepted) answers, and there's the CC-SA license to consider, so -- quite aside from what is technically possible -- my question is when it's permitted to delete your own answer.  Some cases to consider:   You now believe the answer is incorrect. Your answer is correct, but another answer covers the same territory better. You aren't satisfied with the quality/rigor of your answer, e.g. it's speculative and you didn't back it up (on a site that expects that). Something in the answer embarrasses you and you'd rather just make it go away. Your answer wasn't well-received by the community (whether that's "meh" or "make the rep bleeding stop please"). (I'm sure there are others; this isn't meant to be an exhaustive list.)   Does voting matter, either in absolute terms or in comparison to other answers?  For example, maybe it's ok to delete a lower-voted one but not the top-voted answer, or one with score > N??  There is a badge, Disciplined, for deleting your own post of score 3 or higher.  This tells me that it's sometimes ok to delete upvoted answers.  But I'm not sure how much policy we can infer from badges.  Could we have some clarification please? Help me understand the proof for Bolzano-Weierstrass Theorem! Can't install rtl8192eu-linux-driver on UBUNTU 18.10 Does "Erase Disk and Install Ubuntu" replace the default boot screen? I am new here. And I may replace a laptop's hard disk with Ubuntu. It's an HP Compaq notebook which has Windows 7 installed. So If I choose that install option, will it replace the screen that says F12 for boot options [actually it was esc]. I am just asking. I know that choosing that options erases your other partitions. I am assuming it gets replaced by grub2? How to log commands within a "sudo su -"? If I:   [user@notebook ~] sudo echo 123456uu 123456uu [user@notebook ~]    Then I can see that in the logs:  [root@notebook /var/log] grep 123456uu * auth.log:Jan  9 17:01:51 notebook sudo: user : TTY=pts/3 ; PWD=/home/user ; USER=root ; COMMAND=/bin/echo 123456uu [root@notebook /var/log]    but if I:   [user@notebook ~] sudo su - [root@notebook ~] echo 1234567zz 1234567zz [root@notebook ~]    I cannot see it in the logs:   [root@notebook /var/log] grep 1234567zz * [root@notebook /var/log] echo $? 1 [root@notebook /var/log]    My question: How can I turn the logging on for the commands within the "sudo su -"?  OS is an Ubuntu 12.04 but the question is in general.   UPDATE#1:   [user@notebook ~] sudo su - [sudo] password for user:  [root@notebook ~] echo zizizi zizizi [root@notebook ~] cd /var/log [root@notebook /var/log] grep -iIR 'zizizi' * [root@notebook /var/log] grep 'COMMAND=/bin/su -' * auth.log:Jan 10 15:42:42 notebook sudo: user : TTY=pts/1 ; PWD=/home/user ; USER=root ; COMMAND=/bin/su - [root@notebook /var/log] I was recently invited to join InitiativeQ via a friend on Facebook. The underlying idea makes rough sense to me (as a non finance expert). However their 'hook' seems to be that early adopters will get free money later down the line when the currency launches (the earlier you adopt, the more currency you will receive). Looking at the website, there is a big button with the text Reserve $128,957 (I assume that's their idea of what the dollar value of my reservation will be if it launches).  The website's production quality suggests it is not a scam, however the language suggests strongly that it is. Is this a scam, a get rich quick scheme? Or am I being overly paranoid? I have noticed a significant number of suggested edits that attempt to fix code, or change the original meaning of someone else's post.    Is this really a good idea?    I've been on StackOverflow awhile, and among the editors who have sufficient reputation to edit without approval, I've never seen anyone modify the technical content or meaning of someone else's post.   I would consider obvious syntax and spelling errors OK to change, but I have seen many suggested edits that change the meaning of the code that was posted, or add things to the code that have nothing to do with the original question. A good example of this would be adding parameters to a SQL command, when the question was not asking about SQL injection. Taylor expansion for $\arcsin^2{x}$ I stumbled upon this particular expansion that was included in  post.    $$ \displaystyle \arcsin^{2}(x) = \frac{1}{2} \sum_{n=1}^{\infty} \frac{1}{n^{2} \binom{2n}{n}} (2x)^{2n}$$    This caught my eye because I remember trying to derive a Taylor series for $\arcsin^{2}(x)$ a while ago without much success.  Can anyone prove this or point me to a material that would show a proof of this identity?  EDIT :  Feel free to use any mathematical apparatus at hand. I'm not interested in a proof fit for a certain level, nor am I looking for utmost elegance (though that would be lovely). It is common to see things described as the &quot;gold standard&quot;. It means that something is the best and is the ideal against which other things are to be compared; it cannot be superseded. I often , where a certain diagnostic test (e.g., the nasopharyngeal swab PCR test for infection with the Coronavirus causing COVID-19) is considered the most accurate and then other tests (e.g., cheaper or faster tests) are then evaluated against this benchmark. The etymology is covered in . In short, it is derived from the . Thus gold was the thing against which the value of all other currencies was measured. I don't like this term and would like to avoid using it. First, the desired meaning is not predominant; if you  you will mostly get results for the monetary system, not the more general phrase. Second, the etymology is outdated; the original meaning of the term now has the opposite connotation. The monetary gold standard was abandoned in the 1970s. Economists consider the gold standard to be a bad monetary system. Thus, if you are interested in economics and history, the term &quot;gold standard&quot; actually is associated with being outdated and flawed -- which is close to the opposite of the intended meaning. (Of course, many people are unaware of the original meaning of the term. ) (A note in response to comments: Why I want to avoid this term is relevant, but not essential, to the question. If you don't see a problem with the term, the question can be answered regardless.) My question: Is there a better phrase to use in place of &quot;gold standard&quot;? For example, what term could be used in a medical study comparing a new diagnostic test against the gold standard test? I'm not aware of any good substitute that has essentially the same meaning. Here are two example sentences where I would like a replacement:   A nasal swab is the gold standard for diagnosing COVID-19.     The  served as the gold standard for all scales from 1889 until 2019.   The best substitute I can think of is &quot;official,&quot; as in &quot;a nasal swab is the official way to diagnose COVID-19&quot;. &quot;Official&quot; implies some form of uniqueness. But &quot;official&quot; implies the existence of some authority that gives it this designation (as opposed to scientific consensus). A  asks for a &quot;perhaps humorous&quot; alternative -- the suggestion there, &quot;mother of all&quot;, is not appropriate here. (There is also .)  In response to the answers and comments doubting the premise of this question: I personally have a negative association with the phrase &quot;gold standard&quot; because I know people who advocate for returning to the gold standard or its modern equivalent, , and have discussed the topic at length. Several  US  continue to advocate for a return to the gold standard. Thus asserting that no one will interpret the phrase in terms of monetary policy is simply not convincing. Can I use my laptop as a second monitor? I know that I have to use some tweaking tool and then a extension for this. But all extensions that are suggested for this(Workspace grid, Workspace matrix), aren't available in the software center.