1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help with index notation

  1. Oct 9, 2004 #1
    hello, i just started learning index notation in my engineering class, and im having some trouble. one of the problems on my hw was:

    putting this in index notation:
    [tex]\vec{f}=g \frac{m_1m_2}{\vec{r}^2} \ \frac{\vec{r}}{\sqrt{\vec{r}^2}}[/tex]

    and then another problem that reads...

    consider a plane with outer normal vector [tex] v_i [/tex] on which a force is acting [tex] f_i [/tex]. what are the normal components of force on the surface? wut is the max shear component? what direction is the max shear component pointing? write this in index notation.

    i can figure out the components...just not how to write them in index notation. so any help here would be appreciated. thanks
     
    Last edited: Oct 10, 2004
  2. jcsd
  3. Oct 9, 2004 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    For your f, you may write:
    [tex]f_{i}=\frac{Gm_{1}m_{2}}{r_{j}^{2}}\frac{r_{i}}{\sqrt{r_{k}^{2}}}[/tex]
    I read "g" as "G" ; hope I was right about that..:wink:
     
  4. Oct 9, 2004 #3

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    [tex]f^a=g \frac{m_1m_2}{(r_b r^b)^{3/2}} \ r^a[/tex]


    Given a vector [itex]\vec f[/itex] and a unit-vector [itex]\hat n[/itex],
    the vector component of [itex]\vec f [/itex] along [itex]\hat n[/itex] is
    [itex](\vec f\cdot \hat n)\hat n[/itex].
    In index notation,
    [itex]( f^a g_{ab} n^b) n^c[/itex], where [itex]g_{ab}[/itex] is the Euclidean metric tensor and [itex]n^a g_{ab} n^b=1[/itex].
     
  5. Oct 10, 2004 #4
    for the problem with the normal vector and external force, arent the components fsin and fcos? how would i turn those into index notation?
     
  6. Oct 10, 2004 #5

    robphy

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    [tex]f^a g_{ab} n^b=\vec f\cdot\hat n =|\vec f | |\hat n|\cos\theta _\text{between f and n }=|\vec f | \cos\theta _\text{between f and n }[/tex]
     
  7. Oct 10, 2004 #6
    hmmmm [tex]g_a_b[/tex] ......that sounds like the matrix [tex]B_i_j[/tex] my prof was talking about. im unfamiliar with the term Euclidian metric tensor...but am i right in calling it a matrix?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Help with index notation
Loading...