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: Express a vector in a rotated coordinate system

  1. Jul 11, 2013 #1
    1. The problem statement, all variables and given/known data

    I have a coordinate system (x', y') and a vector v'=(1, 0) here. There is a different coordinate system (x, y), which is rotated about the y-axis relative to (x', y') by an angle Ω. I am trying to express v' in the system (x, y).

    At first what I tried to do was to rotate v' by an angle Ω around the y-axis by a rotation matrix, but then it occurred to me that this only rotates the vector, it does not express it in the system (x, y). Can I get a hint to how to achieve this?

    Thanks in advance.
  2. jcsd
  3. Jul 11, 2013 #2


    User Avatar
    Science Advisor

    Expressing a vector in a coordinate system that has been rotated by angle [itex]\theta[/itex] is the same as rotating the vector, in the original coordinate system by [itex]-\theta[/itex].

    For example, if I rotate coordinate system x'y' by 90 degrees, counterclock wise, then the new positive x-axis is the old y'-axis and the new positive y-axis is the old negative x'-axis. (1, 0) becomes (0, -1), exactly the same as rotating the vector itself 90 degrees clockwise.
  4. Jul 11, 2013 #3
    I see, that makes good sense. Thanks for helping me out these past days.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted