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Equilibrium of a Rigid Body question

  1. Feb 22, 2008 #1
    The solid uniform disk of radius b shown can turn freely on an axle through its center. A hole of diameter D is drilled through the disk; its center is a distance r from the axle. The weight of the material drilled out is Fwh. Find the weight of an object hung from a string wound on the disk that will hold the disk at equilibrium in the position shown.

    I really can't figure this one out. I use the center as the axle but I can't find what the distance from the axle would be for the center of mass since the hole drilled in moves it from the center. Can anyone give me a hint to get me started?
     

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  3. Feb 22, 2008 #2

    Doc Al

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    Hint: A hole (no mass) can mathematically be thought of as the sum of a positive mass plus a negative mass.
     
  4. Feb 22, 2008 #3
    So I want to set up an equation where the torque from the weight is equal to the torque of the full disk minus the torque of the hole?
     
  5. Feb 22, 2008 #4

    Doc Al

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    The net torque must be zero. The torque from the "negative mass" hole will be in the opposite direction than that of a positive mass "hole".
     
    Last edited: Feb 22, 2008
  6. Feb 22, 2008 #5
    OK so i work out the equation

    (Fw)= - (r/b)(Fwh) sin theta.

    Unfortunately, the answer has it being cos theta as well as there being no negative sign which makes more sense.

    How I worked it out was

    (Fw)(b) sin 90 = torque of the plate with hole = torque of the entire thing - torque of hole

    (Fw)(b) = 0 - (Fwh)(r)(sin theta)

    (Fw)= - (r/b)(Fwh) sin theta

    Where did I go wrong?
     
  7. Feb 22, 2008 #6

    Doc Al

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    The net torque must be zero, so that should be:
    (Fw)(b) sin 90 + torque of the plate with hole = 0
    or:
    (Fw)(b) sin 90 + torque of the entire thing - torque of hole = 0

    That will get rid of the negative sign.

    Why are you using sin(theta)?
     
  8. Feb 22, 2008 #7
    Should it be sin (90 - theta)?

    Edit: I mean sin (90 + theta) which would be equal to cos theta correct?
     
    Last edited: Feb 22, 2008
  9. Feb 22, 2008 #8

    Doc Al

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    I'd say the first, which does equal cos(theta). :wink:
     
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