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Correspond Momentum of a rigid body to rotational forces

  1. Nov 23, 2011 #1
    1. The problem statement, all variables and given/known data:
    I have the momentum acting on the center of mass of a rigid body consisting of 3 bodies.
    I would like to have the corresponding rotational forces (of this momentum) on the 3 bodies.


    2.
    I derive the general form:

    Frot_i= Inertia_i*(RixM)/Total_Inertia*(Ri)^2

    where:
    Inertia_i=mass_i*(RixM)^2
    Total_Inertia=SUM(Inertia_i)



    3.
    First calculate the vectors
    Rix = xi-xc_of_mass
    Riy = yi-yc_of_mass
    Riz = zi-zc_of_mass

    Then calculate the Ri^2:
    =Rix^2 + Riy^2 + Riz^2

    Then calculate the vectors Vi=(RixM):
    Vix=Riy*Mz-Riz*My
    Viy=Riz*Mx-Rix*Mz
    Viz=Rix*My-Riy*Mx

    Then calculate the scalar Si=(RixM)^2

    Si=Vix^2 +Viy^2+Viz^2

    Then I subtitute to the above equation and calculate the rotational forces of each of the 3 beads i in x y z component:
    Frot_ix
    Frot_iy
    Frot_iz

    When I sum up the x component of the force on the three beads I come out with a non-zero number. Shouldn't it be zero? Same is happening with y and z also.
    Frot_1x+Frot_2x+Frot_3x !=0
    Is the equation for calculating the rotational force correct?
    I would be grateful for any reply.

    cheers,
    Chris
     
  2. jcsd
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