Equilibrium of systems in acccelerating frame

AI Thread Summary
The discussion focuses on the application of the D'Alembert principle in analyzing a free body diagram (FBD) in an accelerating frame. The user questions whether it is valid to choose any point for the torque equation, noting discrepancies in solutions based on the pivot point selected. Two torque equations are presented: one about the center of mass and another about the pivot, yielding different results. Additionally, translational equilibrium equations are provided, with the user acknowledging errors made during calculations. The conversation highlights the complexities of torque analysis in non-inertial frames.
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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

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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.
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My other translational equilibrium eqs are:

ma - Nsin(30) + Fx = 0
Fy + Ncos(30) - mg = 0
 
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my mistakes when pressing the calculator )=
 
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