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Changing from cartesian to polar

  1. Sep 15, 2008 #1
    1. The problem statement, all variables and given/known data
    A particle moves in a two-dimensional orbit defined by:
    x(t)= A(2[tex]\alpha[/tex]t-sin([tex]\alpha[/tex]t)
    y(t)= A(1-cos([tex]\alpha[/tex]t)
    a) Find the tangential acceleration a_t and normal acceleration a_n as a function of time where the tangential and normal components are taken with respect to the velocity.


    2. Relevant equations
    x''(t)= A[tex]\alpha[/tex]^2sin([tex]\alpha[/tex]t)
    y''(t)= A[tex]\alpha[/tex]^2cos([tex]\alpha[/tex]t)


    3. The attempt at a solution
    I found both the velocity and acceleration for both x and y vectors given and realize that a(t)= x''(t)i[tex]\widehat{}[/tex]+ y''(t)j[tex]\widehat{}[/tex]
    also I know that:
    a(t)=a_nr[tex]\widehat{}[/tex]+a_t[tex]\phi[/tex][tex]\widehat{}[/tex]
    So I need to find x" and y" in terms of polar to get the answe for a_n and a_t
     
  2. jcsd
  3. Sep 15, 2008 #2
    sorry all these alphas are not supposed to be raised to the power of there previous components. it is supposed to be for example x(t)=A(2*(alpha)*t-sin((alpha)*t).....and so on
     
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