a uniform thin rod of length L and mass m is pivoted at one end the point is attached to the top of a car accelerating at a rate A.(adsbygoogle = window.adsbygoogle || []).push({});

a) what is the equilibrium angle between the rod and the top of the car?

b) suppose that the rod is displaced a small angle phi from the equilibrium derive the equation of motion for phi. Is the equilibrium angle stable or unstable?

I was able to get part a wich using newtons 2nd law for non inertial frames is

tan(equilibrium angle) = g/A.

but i am stuck on part b. I could use the lagrangian method to get phi(double dot) but that would be really messy, and was wondering if there would be a better way of getting it. oh and also he gave the hint to ignore air resistance and that torque= I*alpha.

thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Deriving an equation of motion

**Physics Forums | Science Articles, Homework Help, Discussion**