Correspond Momentum of a rigid body to rotational forces

[_chris_198]

1. Homework Statement :
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

 

[LightHero]

Homework EquationsFrot_i= Inertia_i*(RixM)/Total_Inertia*(Ri)^2The Attempt at a SolutionYes, the equation for calculating the rotational force is correct. The reason why the sum of the x components of the forces on the three beads is not zero is because the total moment of inertia of the system is not equal to the sum of the moments of inertia of the individual beads. This means that the total rotational force will not be equal to the sum of the individual rotational forces.