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Homework Help: Angular Motion

  1. May 28, 2010 #1
    1. The problem statement, all variables and given/known data

    A uniform rod of length 0.750 m and mass 1.20 kg is pivoted at one end by a smooth pin as shown below. The rod is released from the vertical position and given a slight nudge to release it from the vertical position of unstable equilibrium.

    [PLAIN]http://img175.imageshack.us/img175/9820/angacc40pc.png [Broken]

    When the rod is horizontal:

    (a) Calculate its angular acceleration.

    (b) Calculate the x and the y components of the acceleration of the centre of mass.

    3. The attempt at a solution

    First I focus on part (a). I have already obtained the angular velocity:

    The potential energy of the system relative to the reference configuration is MgL/2 because the center of mass of the rod is at a height L/2 away from its position in the reference configuration. Conservation of mechanical energy for the system is:

    Ki+Ui = Kf + Uf

    0+½MgL=½Iω²+0

    [tex]\omega = \sqrt{\frac{MgL}{\frac{1}{3}ML^2}} = \sqrt{\frac{3g}{L}}[/tex]

    using the given values I get ω=6.26 rad/s, which is the correct velocity.

    Now I want to use the equation [tex]\alpha = \frac{\Delta \omega}{t}[/tex] to find the angular acceleration. Here's where I'm stuck. Could anyone please show me how to find the time for this equation?

    Correct answer to part (a) is 19.62 rad/s² and for part (b) it is -14.7 m/s²(x-component) and -7.36 m/s² (y-component)
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. May 28, 2010 #2

    ehild

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    Homework Helper

    No, you can not use

    [tex]
    \alpha = \frac{\Delta \omega}{t}
    [/tex],
    as it is valid for uniform acceleration only, and you do not know if the acceleration is uniform; neither you know the time.

    There is a formula betwee torque, angular acceleration, and moment of inertia. Use that.

    ehild
     
  4. May 29, 2010 #3
    Thank you very much, I got it. Now could you explain how to deal with part (b)? How do we calculate the x (or y) component of the acceleration of the centre of mass? I'm not quite sure what that even means since I don't have any worked examples in my textbook.
     
  5. May 29, 2010 #4

    ehild

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    The centre of mass moves along a circle, and the angular velocity is not constant. What components of acceleration has a body performing circular motion?

    ehild
     
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