Let's say I have a 1 meter steel rod floating in the vacuum of deep space far from any significant gravitational force, and at rest relative to myself.  Say I apply some force perpendicular to it and near one end:  |==============|   ^   |   |   Clearly the bar will remain within the plane of the bar and the force.  Within that plane, will the rod rotate about its center of mass, move entirely together with some veloctiy in the direction of the force, or a little of both?  If a little of both, how can we calculate how much of each as a function of the strength of the force?
Assume there is a rigid body in deep space with mass $m$ and moment of inertia $I$. A force that varies with time, $F(t)$, is applied to the body off-center at a distance $r$ from its center of mass. How do I calculate the instantaneous acceleration, rotational acceleration, and trajectory of this object, assuming it starts from rest?
Get a list of dates between two dates Using standard mysql functions is there a way to write a query that will return a list of days between two dates.  eg given 2009-01-01 and 2009-01-13 it would return a one column table with the values:   2009-01-01   2009-01-02   2009-01-03  2009-01-04   2009-01-05  2009-01-06  2009-01-07  2009-01-08   2009-01-09  2009-01-10  2009-01-11  2009-01-12  2009-01-13   Edit: It appears I have not been clear. I want to GENERATE this list. I have values stored in the database (by datetime) but want them to be aggregated on a left outer join to a list of dates as above (I am expecting null from the right side of some of this join for some days and will handle this). Why is "If ψ ∈ Γ then the sequent (Γ ⊢ ψ) is correct" true? In Chiswell and Hodges Mathematical Logic the authors define a sequent as such      "A sequent is an expression   (Γ ⊢ ψ) (or Γ ⊢ ψ when there is no ambiguity)   where ψ is a statement (the conclusion of the sequent) and Γ is a set of statements (the assumptions of the sequent) ...There is a proof whose conclusion is ψ and whose undischarged assumptions are all in the set Γ.".   They then go on to provide the axiom as follows:     Sequent Rule (Axiom Rule) If ψ ∈ Γ then the sequent (Γ ⊢ ψ) is correct.   Upon further reading about what exactly it means to be a sequent  I understand that for $\psi$ to be satisfied or "correct", every element of   $\Gamma$ must be true as their all linked by AND conjunctions.    What confuses me is that suppose that there is an element in $\Gamma$ which is false then the whole antecedent is false according to the wikipedia definition by conjunction and then even though $\psi$ exists and is true in $\Gamma$ ultimately $\psi$ would be false. Could someone please explain to me and help clarify how the axiom and the definition can both be true. Thank you for all of your help. Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law] It's so cool that the notification reminds you of the colour of badge you've earned. But I am a little puzzled by the symbols:      Is it feasible to use the symbol from the earned site? At the moment it uses the symbol from the site I happen to be on (as you can see by looking to the left of the dropdown in each case.) Every convergent sequence in a metric space has a unique limit. Does the order of declaration matter in Java/C#? A stranger told me that he will give me an allowance of $ weekly. I know the saying "If it sounds too good to be true, then it is".   He told me that he would  email me his check and I would be able to deposit it via mobile banking. The only information he needs is my email, name on bank account, and bank name.   Is this too much information? Do you think this is a scam? I would definitely know if it was a scam if he asked for my log in but that is not what he wants.  Thank you for your time and answers! My fiancée and I are looking for a good Caribbean cruise in October and were wondering which islands are best to see and which Cruise line to take?  It seems like a lot of the cruises don't run in this month due to Hurricane season so I'm looking for other good options.  EDIT We'll be travelling in 2012. Determining the Orbits/Orbit Space of $O(3)$ on Real 3 by 3 Traceless Symmetric Matrices Let $O(n)$ be the set of $3 \times 3$ orthogonal matrices, and $S$ be the set of traceless real symmetric $3 \times 3$ matrices.  Now  $O(n)$ will act on $S$ by conjugation. Note that by the spectral theorem $ \forall A \in S$ in the orbit of $A$ there is a diagonal matrix $D=diag(\lambda_1, \lambda_2,\lambda_3)$ with $\lambda_1\le\lambda_2 \le\lambda_3 $.  Determine the all the orbits of the action &amp; the orbit space of the action.  What I've done:  Since all elements of $S$ are diagonlizable that the orbit of any element should be the orbit of its' diagonalized form because $\forall A \in S,   \exists P \in O(3)$ st  $PAP^t=D $ with $D$ a diagonal matrix and moreover for any other  $Q\in O(3)$ we get $QDQ^t=QPAP^tQ^t=(QP)A(QP)^t=RAR^t$.   And so would that imply the orbit space is just the set of traceless diagonal matrices as $tr(QDQ^t)=tr(DQ^tQ)=tr(Q)$ (cyclic property of trace) and $Q\in S$.  Any help is appreciated. What's different about photographing at sunrise vs. sunset? I usually get better light at sunrise (compared to sunset). I do though hate to wake up early in the morning to use that light ;)  What are the biggest differences between sunrise and sunset? When performing k-fold cross validation, I understand that you obtain the accuracy metrics by pointing all the folds except one at that one fold and make predictions, and then repeat this process $k$ times.  You can then run accuracy metrics on all of your instances (precision, recall, % classified correctly), which ought to be the same as if you calculated them each time and then averaged the result (correct me if I'm wrong).  The end result you want is a final model.  Do you average the models obtained to make your set of $k$ predictions to end up with the model that has the accuracy metrics obtained by the above method? ArcGIS Python Tool - Importing Custom Script Into ToolValidator Class Syntax highlighting in app differs from normal web view Google map signed api key errors in Android How to type an inline chi in Latex \( \chi \) produces a letter that is slightly below the row, but I've seen in many papers a chi that is in the same line as the rest of the row) How is Clan War Map position determined? Is there a reasonable statistic test one can do to standard random number generators (say, one of those that come built in in Python libs) which shows they are not really random?  (By reasonable I mean to exclude silly things like «generate a looong list and see that it is periodic»)  Later: Notice I am looking for a test that fails on standard generators. 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? I see the  on the user page.  It seems to edit posts sometimes.  What is it? And why has it downvoted over 1800 times? See also: Security Review - CRUD/FLS Checks for every SOQL Query I know this sounds like a standard question, so please bear with me.  Recently our Security Reviews fail due to CRUD/FLS violations. The highlighted codelines include almost every SOQL Query in the application.  Our approach is usually as follows:   In case of displaying data on VF pages we either use sObjects fields or use the platform methods to check the accessibility of the fields In case of domain logic triggered by the user (e.g. by clicking a button on a VF page) we have a helper class that checks every field to be updated before doing the DML operation.   Up until recently this approach has worked fine (and passed pervious Security Reviews). As mentioned above the latest Security Review results seem to require us to check every field in a SOQL query for accessibility even if it is never displayed back to the user.    Let's suppose the following program flow as an example:   Query an object with some fields Perform some modification on said fields Perform an update on the sObject to save the modification using a helper class which checks for the required CUD/FLS rights for the modified fields   As I see it there is no need for checking field accessibility in step 1 in that case (since nothing is displayed back to the user and the dml operation is already protected). Is that correct or am I missing something? So is it really required to do an accessibility check for every SOQL Query in the code?  Another question would be how to handle background operations in that case like data purging. These have either to be running in system mode (which causes issues during the Security Review) or require the job to be started by a user with the appropriate access rights (which can be error prone and is not that user friendly). Is there any best practice regarding that.  Unfortunately I could not find a question targeting exactly that issue. Most of the questions I have found are related to how to perform that check (like  or ). So please apologize in case the question was already answered (I would really appreciate a link to the answer then).    Thanks for your time and help.  Mathias