Equilibrium of systems in acccelerating frame

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SUMMARY

The discussion centers on the application of the D'Alembert principle in analyzing the equilibrium of systems in an accelerating frame. The user presents two different torque equations derived from a free body diagram (FBD), one about the center of mass (CM) and the other about a pivot point. The equations yield different solutions, prompting a query about the validity of choosing any point for torque calculations. The user also shares their translational equilibrium equations, highlighting a calculation error as the source of discrepancies in their results.

PREREQUISITES
  • D'Alembert principle in mechanics
  • Understanding of torque and its calculation
  • Free body diagram (FBD) construction
  • Basic principles of translational equilibrium
NEXT STEPS
  • Study the implications of choosing different pivot points in torque calculations
  • Learn about the D'Alembert principle applications in dynamic systems
  • Explore advanced techniques for constructing free body diagrams
  • Investigate common mistakes in equilibrium calculations and how to avoid them
USEFUL FOR

Students and professionals in physics and engineering, particularly those focusing on mechanics and dynamics of systems in non-inertial frames.

serverxeon
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I've drawn the following FBD (using D'alembert prinicple)
[The N in my drawing is the F_A stated in the question]

579kn.jpg

----------------

Assuming my FBD has nothing wrong, am I right to say that I am free to choose my torque equation about ANY POINT?

somehow my solutions vary depending on my point of consideration.

Torque eq about CM:
N + 2Fy cos(30) -2Fx sin(30) = 0

-or-
or eq about pivot:
N - 2mg cos(30) - 2ma sin(30) = ma

It just doesn't give the same solution.
--------------------------------------------
My other translational equilibrium eqs are:

ma - Nsin(30) + Fx = 0
Fy + Ncos(30) - mg = 0
 
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solved.

my mistakes when pressing the calculator )=
 

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