Understanding Moment Equations in Rigid Body Equilibrium

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SUMMARY

The discussion centers on the moment equation "NA*a - F*b = 0" in the context of rigid body equilibrium. Participants clarify that forces Nb and Nc are excluded from the moment calculation because their lines of action pass through the pivot point, resulting in zero torque. The importance of understanding the moment arm and its relationship to the axis of rotation is emphasized, as forces that do not create a perpendicular distance from the pivot do not contribute to the moment. This foundational concept is crucial for accurately analyzing moments in rigid body mechanics.

PREREQUISITES
  • Understanding of rigid body equilibrium principles
  • Familiarity with moment calculations and torque
  • Knowledge of force vectors and their components
  • Basic grasp of physics concepts related to rotation
NEXT STEPS
  • Study the concept of moment arms in rigid body mechanics
  • Learn about calculating torque from various force orientations
  • Explore the implications of force lines of action on moment calculations
  • Investigate advanced topics in static equilibrium analysis
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Students and professionals in mechanical engineering, physics educators, and anyone involved in analyzing rigid body dynamics and equilibrium conditions.

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I have uploaded the question with solution at this address: http://i41.tinypic.com/o5xm5j.jpg

All I need to know is why in the moment equation "NA*a - F*b = 0" the forces Nb and Nc aren't included. Is it because the moment is being calculated about the dot in the middle, and the other two forces are pointing at it?
If the Nc force wasn't pointing directly at that center point (and was pointing slightly above), would I have to calculate the net moment including the horizontal and vertical components of Nc from point C?
When do I know not to include a force in the moment calculation?

Thanks!
 
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If the of the force passes through the axis then it doesn't exert any torque on the axis. Think of it as how would the torque rotate about the given axis ;)
 
Your assumption is right, you do not include it because the line of action of that force goes through the point around which you calculate the moment. If it goes through it then the perpendicular distance from the line of action to the point, moment arm, would be zero. Intuitively you can also see that it just wouldn't cause any rotation.
 
I guess I got so caught up in formula's 'n such that I forgot what was really going on.

Thank you both!
 

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