Linear fictitious force problem

  • #1
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Homework Statement


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Homework Equations




The Attempt at a Solution


I understand the solution of the problem, but I want to know why don't my approach work.

I didn't change the frame of reference.
I use the regular method of solving a torque problem.
(mgsinθ - mAcosθ)(L/2) = mL2/3 θ''
which is approximately equal to
gθ-A = 2/3 L θ''
by solving differential equations, I got a frequency of Root (3/2 * g/L) , why am I wrong? Thank you (Also, isn't the moment of inertia of a rod 1/3 * mL^2 with respect to the rod?)
 

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Answers and Replies

  • #2
Charles Link
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Yes, the moment of inertia of the rod about the pivot point is ## I_a=\int\limits_{0}^{L} \rho \, r^2 \, dr =(\frac{1}{3})ML^2 ##. ## \\ ## That will get you the correct answer. ## \\ ## ( It's only ## (\frac{1}{12})ML^2 ## if you rotate it about its center).
 

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