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Uniform Circular Motion

  1. Oct 7, 2004 #1
    Hi, I'm having trouble on a set of problems and I was wondering if someone could walk me through how to do one of these so I can at least attempt the rest. The problem says:

    "A point P moves uniformly along the circle x[squared] + y[squared]= r[squared] with constant agular velocity w. Find the x and y coordinates of P at time t given that the motion starts at time t=0 and [theta] = [theta]initial. Then find the velocity and acceleration of the projection of P onto the x axis and onto the y axis."

    I found the derivitive of the equation that was given but I have no idea where to go from there. Thank you for your help.
     
  2. jcsd
  3. Oct 7, 2004 #2

    arildno

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    Welcome to PF!
    How do you parametrize a circular trajectory?
     
  4. Oct 7, 2004 #3
    what do you mean exactly? there's another little note on the problem that says the projection of p onto the x azis is the point (x,0) and the project of p onto the y axis is the point (0,y)
     
  5. Oct 7, 2004 #4

    arildno

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    Do you agree that since the particle moves in a circular orbit, we may write:
    [tex]x(t)=r\cos(f(t)),y(t)=r\sin(f(t))[/tex]
    where f(t) is as yet undetermined.
    With this choice, we are guaranteed that the particle moves on a circle, since:
    [tex]x^{2}(t)+y^{2}(t)=r^{2}[/tex]
     
  6. Oct 7, 2004 #5

    arildno

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    If you agree so far, let's determine f(t)!
    We know that the speed must be rw, since w is the constant angular velocity.
    Differentiating to gain the velocity, we end up with the speed equation:
    [tex]r|f'(t)|=rw[/tex]
    agreed? (|| signifies the absolute value)
    This means f(t)=wt+K, where K is some constant.
    If you have some particular questions to this, post them
     
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