# Correspond Momentum of a rigid body to rotational forces

1. Nov 23, 2011

### _chris_198

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