# Reaction forces due to imbalance of a shaft

**1. The problem statement, all variables and given/known data**

The shaft carries two particles of mass m, and rotates about the z-axis with the constant angular velocity ##\omega##. Determine the x- and y-component of the bearing due to imbalance.

**3. The attempt at a solution**

Rotation only around the ##z-##axis so ##\omega _{x}=\omega _{y}=0## and ##\boldsymbol{\omega }=\omega \boldsymbol{\hat{k}}##. Since ##\dot{\omega}=0## we have:

##\left\{\begin{matrix}

\sum M_{x}=I_{yz}\omega^2\\ \sum M_{y}=-I_{xz}\omega^2

\\

\end{matrix}\right.##

I have trouble now. Is it correct that for ##M_{y}##, only forces acting **perpendicular** to y-axis that should be accounted for? We also see that the intersection of points of the ##xz-##plane and the two sphere’s are none so that means that ##I_{xz}=0##(Is this even correct??). And ##I_{yz}=\overline{I}_{yz}+md_{y}d_{z}=0+mR\frac{L}{3}-mR\frac{2L}{3}##

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