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Circular Motion of a Particle

  1. Sep 19, 2008 #1
    1. The problem statement, all variables and given/known data

    The circular motion of a particle in the x-y plane is given by the equations: r(t)= 6.46 m, theta (t)= (6.96 rad/s) t, where r is the distance from the origin and theta is the polar angle measured counterclockwise from the positve x-axis. Calculate the x-coordinate of the particle at time t= 4.00s

    2. Relevant equations

    I can visualize it, but can't put the steps togather to solve it. I know I have to find out what angle the position vector is pointing at, then solve for t. The distance from the center of the point probably won't vary with t right?
     
  2. jcsd
  3. Sep 19, 2008 #2
    "I can visualize it, but can't put the steps togather to solve it. I know I have to find out what angle the position vector is pointing at, then solve for t. The distance from the center of the point probably won't vary with t right?"

    Find theta when t = 4, then use the transformation equation x = r cos theta.

    Yes, the particle moves on a circular path around the origin.
     
  4. Sep 19, 2008 #3
    Thanks for your help! but how do I find theta?
     
  5. Sep 19, 2008 #4
    Wait I plugged in four or t and got 27.84 for theta which I then plgged into my x= r. cos (theta) formula and got 8.36 m which is not the right answer.....
     
    Last edited: Sep 19, 2008
  6. Sep 19, 2008 #5

    cepheid

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    You made a mistake with the computation of x. You can see that immediately...because your calculated value for the x-coordinate is *greater* than the radius! (That makes absolutely no sense). I would recalculate rcos(theta).
     
  7. Sep 19, 2008 #6
    I did it agai and got 5.71 which is still wrong...
     
  8. Sep 19, 2008 #7
    Theta is in radians, not degrees. Check which mode your calculator is in.
     
  9. Sep 19, 2008 #8

    cepheid

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    That's not very helpful to us. You should POST your work so that we can see if there is some sort of error. In this case, it's a question of punching a few buttons on your calculator and getting the result. There is not much opportunity for error. So here's what I'm going to do. Answer these questions:

    1. What is the cosine of 27.84 (IS YOUR CALCULATOR IN RADIAN MODE?)

    2. What is r times the cosine of 27.84 (i.e. what is 6.46 * the result of part 1)?
     
  10. Sep 19, 2008 #9
    -5.86
     
  11. Sep 19, 2008 #10
    i'm sorry guys i'm really sleep deprived thanks
     
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