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Uniform circular motion of a particle problem

  1. Jun 23, 2015 #1
    1. The problem statement, all variables and given/known data
    A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.30 s, it is at point (5.10 m, 6.80 m) with velocity (3.90 m/s)## \hat j ## and acceleration in the positive x direction. At time t2 = 9.90 s, it has velocity (–3.90 m/s)## /hat i ##and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit.

    2. Relevant equations
    a=v2/r, v=2πr/T,



    3. The attempt at a solution
    hMthL4b3OjGjbIWmGkYHA%2F12%2F424149441%2Fjpeg%2F32x32%2F1%2F1435046400%2F0%2F2%2F20150622_205717.jpg
     
  2. jcsd
  3. Jun 23, 2015 #2

    tony873004

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    If all its speed is in j-hat while at (5.1, 6.8), then it is crossing the horizontal axis through the circle at that moment. Hence, the y-component of the center is the y-component of (5.1,6.8)

    It’s tangential speed is 3.9 m/s. It takes 9.9-3.3 seconds to travel ¼ around its orbit. (I’m assuming it didn’t go 5/4, or 9/4 around, etc.). So now you have a speed and a time, so you can solve for distance (circumference). Then it’s easy to get radius. If you know the radius and you know its position when all its velocity in is the j hat direction, then your radius is the offset from you x-component of that position.
     
  4. Jun 23, 2015 #3
    would'nt it travel 3/4 around the circle 3pi/2 if its velocity is positive jhat at the left side of the circle its moving clockwise?
     
  5. Jun 23, 2015 #4

    tony873004

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    Is it given that its moving clockwise?
     
  6. Jun 23, 2015 #5
    no but both vectors are pointing in a direction that would indicate clockwise motion
     
  7. Jun 23, 2015 #6

    tony873004

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    You're right, it moves 3/4 around.
     
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