1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: How do you prove that a=-(w^2)

  1. Feb 6, 2006 #1
    how do you prove that a=-(w^2)
    from v=wxr?
    i know you're supposed to differentiate v=wxr, but i don't know how to differentiate a cross product...
    Last edited by a moderator: Jan 7, 2014
  2. jcsd
  3. Feb 6, 2006 #2
    The cross product is the vector created by the determinant
    [tex] a \times b =
    \begin{tabular}{|c c c|}
    i & j & k \\
    a_1 & a_2 & a_3 \\
    b_1 & b_2 & b_3 \\

    So, take the determinant of the above matrix, and then differentiate as normal. (Hint: the determinant will give you a vector, with 3 coordinates. You can differentiate each coordinate on its own.)

    Edit: are you familiar with how to take a determinant? Otherwise you can use [itex]a \times b = |a||b|\sin{\theta}[/itex], but then you'll have to know [itex]\theta[/itex], or treat it as a constant.
    Last edited: Feb 6, 2006
  4. Feb 7, 2006 #3
    thank you very much!!!
    what happens if you want to prove it for an infinite number of coordinates(ex., i, j, k, l, m, ....)?
  5. Feb 7, 2006 #4


    User Avatar
    Science Advisor

    The cross product is only defined in R3.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook