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Homework Help: Non-Uniform Circular Motion problem

  1. Sep 24, 2010 #1
    "Non-Uniform Circular Motion" problem

    1. The problem statement, all variables and given/known data
    A ball swings in a vertical circle at the end of a rope 1.50 m
    long. When the ball is 36.9° past the lowest point on its
    way up, its total acceleration is (-22.5 i + 20.2j) m/s^2. At
    that instant, (a) sketch a vector diagram showing the components
    of its acceleration, (b) determine the magnitude
    of its radial acceleration, and (c) determine the speed and
    velocity of the ball.

    2. Relevant equations
    a = v^2 / r
    a(total) = a(tangent) + a(radial)

    3. The attempt at a solution
    For starters, I don't even know how to approach a), in all honesty. Since the problem doesn't tell me in which direction the rope is spinning, I don't know where to start. However, I have a feeling that the problem doesn't need to tell me this based on the information regarding total acceleration.
    Also, even though the total acceleration is expressed in that format, I seriously doubt that the unit vectors are ar and at. If I knew how to draw this, I'll probably be able to figure out the rest of the problem...
  2. jcsd
  3. Sep 24, 2010 #2
    Re: "Non-Uniform Circular Motion" problem

    It's a vertical circle.There is the weight of the ball downwards and tension of string at an angle.
    And yes the unit vectors i and j are not along the radial and transverse directions. If you would draw the problem keeping in mind that the plane of the circle is vertical it would be easier.
  4. Sep 24, 2010 #3
    Re: "Non-Uniform Circular Motion" problem

    All right, I get that much. However, I'm still unable to determine if it's 36.9o to the left, or to the right.....
  5. Sep 25, 2010 #4
    Re: "Non-Uniform Circular Motion" problem

    How does it matter?
  6. Sep 25, 2010 #5
    Re: "Non-Uniform Circular Motion" problem

    [PLAIN]http://photos-a.ak.fbcdn.net/hphotos-ak-snc1/hs030.snc1/3190_91017112564_509877564_2512520_5779508_n.jpg [Broken]

    According to this solution, it does...
    Last edited by a moderator: May 4, 2017
  7. Sep 25, 2010 #6
    Re: "Non-Uniform Circular Motion" problem


    I don't mean to offend anybody, but can anyone explain why the solution goes 36.9 degrees to the right, and no to the left?
  8. Sep 26, 2010 #7
    Re: "Non-Uniform Circular Motion" problem

    If you were to look at the setup from the other side the rope would go left. If the diagram is already sketched there is no harm in referring the directions as left or right for convenience.
  9. Sep 26, 2010 #8
    Re: "Non-Uniform Circular Motion" problem

    So you're saying that I could draw it in either direction, and I could still get the diagram, along with b) and c) correct. Am I following you correctly?
  10. Sep 26, 2010 #9
    Re: "Non-Uniform Circular Motion" problem

  11. Sep 27, 2010 #10
    Re: "Non-Uniform Circular Motion" problem

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