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Moment of inertia for non homogeneous density.

  1. Mar 6, 2012 #1
    Ok so I am trying to figure how I would find the moment of inertia for a special case. I have a 55 gallon barrel that is almost half way full and I am suppose to spin it roughly 5-10 rpm.

    I know that to find the momement of interia of a hollow cylinder with thick walls is simply
    I = 1/2M(r(1)^1+r(2)^2) yet this equation is too simple for this situation

    I also know that
    I = ρ ∫r^2 dV However this is for a homogenous density, which is not this case.

    I am wondering what is the best way to find the moment of intertia for a non uniform density.

    I have attached a picture for clarity.

    Thanks for reading.

    Attached Files:

  2. jcsd
  3. Mar 7, 2012 #2


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    Hi Teachme! :smile:

    I don't understand :redface:

    if the barrel is rolling (in place) as shown in the diagram, then why would the fluid rotate at all (and so why would you need its moment of inertia)? :confused:
  4. Mar 7, 2012 #3
    I think you are right. Since the fluid has no speed you are saying it does not add to the moment of inertia?. I am trying to find the total kinetic energy of the barrel and the fluid in the barrel when it is spinning 5rpm. I know that I need the moment of inertia to find the total kinetic energy... So how would I go about incorporating the the fluid inside the barrel effect my situation? Would I have to use torque for this? My final goal is finding what size motor i need to get it to spin. (not my question however).

    Thank you again for your help, I appreciate it very much.
  5. Mar 7, 2012 #4


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    Well, the fluid will still slosh about a bit, so it'll have some kinetic energy, and also there'll be heating from the friction between the fluid and the barrel.

    I think the only way you could find that is to carry out experiments, and actually measure either the power needed or (for example) the temperature rise in the fluid.
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