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A triangle's rotational kinetic energy

  1. Apr 2, 2008 #1
    1. The problem statement, all variables and given/known data
    The three 300 g masses in the figure are connected by massless, rigid rods to form a triangle.
    [​IMG]

    What is the triangle's rotational kinetic energy if it rotates at 8.00 revolutions per s about an axis through the center?

    Values given:
    Mass of each ball at the corner of the triangle: 0.3 kg
    Sides of Equilateral Triangle: 0.4m
    It is rotating at 8.00 revolutions per second

    2. Relevant equations
    I= (m)(r[tex]^{2}[/tex]) + (m)(r[tex]^{2}[/tex]) + (m)(r[tex]^{2}[/tex])
    K[tex]_{rot}[/tex]=(1/2)Iw[tex]^{2}[/tex]

    3. The attempt at a solution

    First thing i did was try to find the radius of the triangle. I cut it in half down the middle, making a right angle with a side of .2m and a hypotenuse of .4m.

    (0.2[tex]^{2}[/tex]) + (height[tex]^{2}[/tex]) =(0.4[tex]^{2}[/tex])
    height = 0.346

    I halved the height to get the radius.

    Radius: 0.173


    Then i used the Equation I= (m)(r[tex]^{2}[/tex]) + (m)(r[tex]^{2}[/tex]) + (m)(r[tex]^{2}[/tex])

    I = (0.3)(0.173[tex]^{2}[/tex]) + (0.3)(0.173[tex]^{2}[/tex]) + (0.3)(0.173[tex]^{2}[/tex])

    I = 0.027

    Then i converted 8 rev per sec into 50.24 rad per sec.

    Then i used K[tex]_{rot}[/tex]=(1/2)Iw[tex]^{2}[/tex]

    K[tex]_{rot}[/tex]=(1/2)(0.027)(50.24)[tex]^{2}[/tex]

    K[tex]_{rot}[/tex] = 136

    I don't know what I'm doing wrong. Please help.
     
  2. jcsd
  3. Apr 2, 2008 #2

    Dick

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    The radius of rotation isn't 0.173m. Think about it. It's the hypotenuse of a triangle, one of whose sides is 0.2m. It should be the distance from the center of the triangle to the rotating masses, not the "height".
     
    Last edited: Apr 2, 2008
  4. Apr 2, 2008 #3
    wouldn't that be .4 then? I don't think I understand what you're trying to tell me.
     
  5. Apr 2, 2008 #4

    Dick

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    The 'r' in your formula should be the distance from the axis to the rotating masses. It isn't 0.173m nor is it 0.4m. Rethink your triangle.
     
  6. Apr 2, 2008 #5
    Thank you. That was a silly place for me to make mistakes.
     
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