Basic non-rotating accelerating reference frame problem

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SUMMARY

The problem involves a uniform thin rod of length L and mass M, pivoted at one end on a car accelerating at rate A. The equilibrium angle θ between the rod and the top of the car can be analyzed by treating the car's acceleration as a horizontal gravitational field of strength A. The solution requires balancing torques about the pivot, considering the forces of gravity and the fictitious force due to the car's acceleration. The user successfully resolved the issue after initial confusion regarding the torque balance.

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  • Familiarity with fictitious forces in non-inertial reference frames
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Homework Statement



A uniform thin rod of length ##L## and mass ##M## is pivoted at one end. The pivot is attached to the top of a car accelerating at rate ##A##. What is the equilibrium value of the angle ##\theta## between the rod and the top of the car?

Homework Equations



None in particular?

The Attempt at a Solution



I understand that we can treat the acceleration of the car as a horizontal gravitational field of strength ##A##. I attempted to solve the problem via torque balance (taking the torque about the pivot), but the only two forces, gravity and the fictional force, have ##\theta## terms that end up cancelling out. I'm sure this is simple, but honestly moving on is going to problem if I can't even do this problem, haha.
 
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Oh, never mind, totally figured this one out.
 

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