Question

Three masses are connected to a rotating shaft supported on bearing A and B as shown in the figure. The system is in a speace where the gravitational effect is absent. Neglect the mass of shaft and rods connecting the masses. For $m_1=10kg,m_2=5kgand{m}_3=2.5$ kg and for a shaft angular speed of 1000 radian/s the magnitude of the bearing reaction (in N) at location Bis

Answer 1

It means all three masses are in same plane let us calculates the net force
$\Sigma F_x=\Sigma mr{\omega }^{2}cos\theta$
$=(10\times 0.1\times {\omega }^2)-(5\times 0.2\times {\omega }^{2}cos{60}^o)$
$-(2.5\times 0.4\times {\omega }^2\cos {60}^o)$
$=[1-(5\times 0.2\times \frac{1}{2})-(2.5\times 0.4\times \frac{1}{2})]{\omega }^2=0$
$\Sigma F_y=\Sigma mr{\omega }^{2}sin{60}^o$
$=(5\times 0.2\times {\omega }^{2}sin{60}^o)-(2.5\times 0.4\times {\omega }^{2}sin{60}^o)$
$=[(1\times \frac{\sqrt{3}}{2})-(1\times \frac{\sqrt{3}}{2})]{\omega }^2$
$=\left[(\frac{\sqrt{3}}{2}-\frac{\sqrt{3}}{2})\right]{\omega }^2=0$
Net force,

$F=\sqrt{\Sigma F_x^2+\Sigma F_y^2}=0$
Therefore reaction at B is zero.
$R_B=0$