Basic non-rotating accelerating reference frame problem

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MuIotaTau
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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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