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Mechanics-Angular Motion and Conservation of Energy

  1. Apr 21, 2012 #1
    Mechanics--Angular Motion and Conservation of Energy

    1. The problem statement, all variables and given/known data

    A uniform bar of mass m and length L is pivoted at one end and is held vertically above the pivot. After the bar is released, it swings downward and clockwise with no friction in the pivot.

    At the instant the bar is horizontal, find the magnitudes of the following quantities (use g for the acceleration of gravity): The horizontal component of the acceleration of the free end of the bar? The vertical component of the acceleration of the midpoint of the bar? The vertical component of the force exerted on the bar by the hinge?

    2. Relevant equations
    Moment of inertia = .33*m*r*r

    3. The attempt at a solution
    There were many other questions in this problem that I already got correct, so I left those out. I used the transfer of gravitational potential energy to rotational kinetic energy to get the angular and linear speeds, and I found the angular acceleration using torque, but I couldn't get these three parts. I feel like the acceleration of the bar in the vertical direction should be zero at this point because it's only accelerating towards the center of the circle, which is horizontal, but it's a nonzero value. Thanks for your help!
     
  2. jcsd
  3. Apr 21, 2012 #2
    Re: Mechanics--Angular Motion and Conservation of Energy

    "I feel like the acceleration of the bar in the vertical direction should be zero at this point because it's only accelerating towards the center of the circle, which is horizontal, but it's a nonzero value. Thanks for your help!"

    Hint: Suppose the bar were released from this point, would it accelerate downward or merely remain horizontal?
     
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