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2-D Acceleration Vector

  1. Sep 18, 2010 #1
    1. The problem statement, all variables and given/known data
    An object is moving along an ellipse which is described by x(t)=acos([tex]\omega[/tex]t) and y(t)=bsin([tex]\omega[/tex]t). Determine magnitude of acceleration vector as a function of parameters a, b, and [tex]\omega[/tex]. Is magnitude of acceleration vector constant over time?


    2. Relevant equations
    r(t)=x(t)x+y(t)y
    v=dx/dtx+dy/dty


    3. The attempt at a solution
    r(t)=acos([tex]\omega[/tex]t)x+bsin([tex]\omega[/tex]t)y
    a(t)=dvx/dtx+dvy/dty
    v=-a[tex]\omega[/tex]sin([tex]\omega[/tex]t)x+b[tex]\omega[/tex]cos([tex]\omega[/tex]t)y
    a=-a[tex]\omega[/tex][tex]^{}2[/tex]cos([tex]\omega[/tex]t)x-b[tex]\omega[/tex][tex]^{}2[/tex]sin([tex]\omega[/tex]t)y=-[tex]\omega[/tex][tex]^{}2[/tex](acos([tex]\omega[/tex]t)x+bsin([tex]\omega[/tex]t)y
    a=-[tex]\omega[/tex]2r(t)
     
    Last edited: Sep 18, 2010
  2. jcsd
  3. Sep 19, 2010 #2

    ehild

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    I assume that you mean the unit vectors along the axes x,y by "x" and "y" and both "r" and "a" are vectors. Your last equation is the relation between the vector of acceleration and the position vector. What is the magnitude of acceleration?

    ehild
     
  4. Sep 19, 2010 #3
    Am I approaching it incorrectly? Both "r" and "a" are vectors. I assume I have to find magnitude of vector "r" but am not certain how to do it.
     
  5. Sep 19, 2010 #4

    ehild

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    Do you know how to calculate the magnitude of a vector from its components?

    ehild
     
  6. Sep 20, 2010 #5
    I believe I calculate it by doing the square root of its components squared. Is that right?
     
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