GATE ME 2017 Set 2 — Question 34
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Theory of Machines & Vibrations → Balancing, Flywheels & Gyroscopes → Balancing of Rotating Masses
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Question
Three masses are connected to a rotating shaft supported on bearings A and B as shown in the figure. The system is in a space where the gravitational effect is absent. Neglect the mass of shaft and rods connecting the masses. For , and and for a shaft angular speed of , the magnitude of the bearing reaction (in N) at location B is 
Correct answer
0 to 0
Solution
The centrifugal force for each mass is given by .Given:
, ,
, ,
, ,
Calculating the product for each mass:
The resultant centrifugal force vector is .
Resolving into components:
Since the resultant force in the plane of the masses is zero and all masses are located in the same transverse plane, the system is both statically and dynamically balanced. Consequently, there are no unbalanced forces or moments acting on the shaft, and the bearing reactions at A and B are zero.
, ,
, ,
, ,
Calculating the product for each mass:
The resultant centrifugal force vector is .
Resolving into components:
Since the resultant force in the plane of the masses is zero and all masses are located in the same transverse plane, the system is both statically and dynamically balanced. Consequently, there are no unbalanced forces or moments acting on the shaft, and the bearing reactions at A and B are zero.
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