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Rotational KE question

  1. Mar 17, 2010 #1
    1. The problem statement, all variables and given/known data

    A thin square slab with sides of length 0.550 m and mass 1.80 kg is suspended so it can freely rotate about a horizontal axis of rotation perpendicular to the surface at one corner. The square is held so its top and bottom edges are horizontal, and then is released. What is the angular velocity of the square when the point opposite the pivot is as low as possible?

    2. Relevant equations

    KE = ½Iω^2
    IP = ICM + Mh^2 (parallel axis theorem)


    3. The attempt at a solution

    I need help setting it up. I feel like I should be determining the angle to find out how far the sheet moved..am I on the right track?
     
  2. jcsd
  3. Mar 17, 2010 #2

    rock.freak667

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    Homework Helper

    The change in potential energy = change in the rotational kinetic energy.

    So you need to find the change in potential energy the center of gravity undergoes from the horizontal position to the lowest position.
     
  4. Mar 17, 2010 #3
    Okay, so setting up the problem...

    ½Iω^2=½mv^2

    So then switching things around I get

    ω^2=(½(1.8)v^2)/(½I)

    So then to find I I use Ip=Icm +mh^2 and h will be the diagonal of the square.
    And for v?? I don't know..
     
  5. Mar 17, 2010 #4

    rock.freak667

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    Not change in translational ke, change in pe.

    At the horizontal position what is the height of the center of mass (COM) of the square? At the lowest point what the height of the COM, both with respect to a line passing through the stationary corner.

    Also what is Ic for the slab?
     
  6. Mar 18, 2010 #5
    So.. ½Iω^2=mgh

    and then for I, I= 1/12 x m (a^2+b^2) + mh^2

    So altogether: ½(1/12 x m (a^2+b^2) + mh^2)(ω^2)=mgh

    For h I used the difference in measurement between the diagonal and side since this seems to me like the distance the square would have fallen.

    I ended up with an angular velocity of 3.153 after plugging everything in but this was incorrect.
     
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