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Homework Help: Rotating coordinates

  1. Dec 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A 2D rotating coordinate system (x,y) is defined by:
    [tex]x=Xcos\omega t+Ysin \omega t[/tex]
    [tex]y=-Xsin\omega t+Y cos \omega t[/tex]

    Where (X,Y) is the coordinate of the inertial frame and omega is some angular frequency. What is the force required to keep a mass m moving in a "straight" line (x,y)=(ut,0) where u is a constant?


    2. Relevant equations
    [tex]F=m\frac{d^2x}{dt^2}[/tex]
    and the given equations of the new coordinates.


    3. The attempt at a solution
    Let me take the derivative of the given equations twice:
    [tex]\frac{d(Xcos\omega t+Ysin \omega t)}{dt}=-X\omega sin \omega t + Y \omega cos \omega t=\omega y[/tex]
    [tex]\frac{d^2x}{dt^2}=\omega \frac{dy}{dt}=\omega \frac{d(-Xsin\omega t+Y cos \omega t)}{dt}= \omega \left ( -\omega X cos \omega t -\omega Y sin \omega t \right)= -\omega^2 x [/tex]
    Similarly:
    [tex]\frac{dy}{dt}=-\omega x[/tex]
    [tex]\frac{d^2y}{dt^2}=-\omega^2 y[/tex]

    So we have:
    [tex]F_x=-m \omega^2x[/tex]
    [tex]F_y=-m \omega^2y[/tex]

    Um... is this some kind of a spring force?
     
    Last edited: Dec 17, 2009
  2. jcsd
  3. Dec 17, 2009 #2

    diazona

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    Homework Helper

    ...did you forget to finish typing out your attempt at the solution?
     
  4. Dec 17, 2009 #3
    ?? Is my Latex showing?
     
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