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Rotating rigid bodies

  1. Jun 10, 2012 #1
    -See attached diagram
    - A uniform disc of mass m and radius a is free to rotate in a vertical plane about a fixed smooth horizontal axis, the axis passes through the mp A of the radius of the disc.
    - It then asks you to dervie equations of motion for when AO makes an angle pheta with the downward vertical ( and to find the force perpendicular to AO when AO is in this position)


    To get the correct solution, the diagram needs to be correct - if I'm correct, as this determines whether the mass is speeding up or down, as if the angle was on the opposite side, the mass would INSTEAD be speeding up - which changes everything.

    I have a few questions in how exactly the question specifies some details of the diagram

    1) The angle with the downward vertical, why is it not the other side - is this convention, as in when they specify pheta with the downward vertical it is the counter clockwise direction.
    2) Why is the angular acceleration not negative - as the body slows down as it goes upward.(Actually, I assume this is relative to the equation itself, as if you did this, you would get the same for Y , taking mg as negative)
    3) To the diagram I have added a direction for the angular velocity - is this correct? Also if you choose to do this, shouldn't the angular acceleration be drawn in the opposite direction?
     

    Attached Files:

  2. jcsd
  3. Jun 10, 2012 #2

    Simon Bridge

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    I don't understand the bit in bold.
    theta
    If I have this right - the disk is hanging from a point on it's edge so it can swing like a pendulum.
    The disk will normally hang motionless if AO is vertical - so this is a natural choice for the zero angle. You can pick anything you like but it makes the math easier if you let the physics suggest the choice.
    Acceleration is a vector. Acceleration can be negative when an object slows down, or if it speeds up in the negative direction.
    Before I can comment properly I need to be sure I have understood what the diagram represents.

    If you displace a pendulum anticlockwise by some angle θ, and let go, it's initial angular velocity will be zero and it's acceleration will be a maximum pointing clockwise. Does that help? From what I understand about this description your disc will behave like a pendulum.
     
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