Two small, equal masses are attached by a lightweight rod. This object orbits a planet; the length of the rod is
smaller than the radius of the orbit, but not negligible. The rod rotates about its axis in such a way that it remains
vertical with respect to the planet.
• Is there a force in the rod? If so, is it tension or compression?
• Is the equilibrium stable, unstable, or neutral with respect to a small perturbation in the angle of the
rod? (Assume this perturbation maintains the rate of rotation, so that in the co-rotating frame the rod
is still stationary but at an angle to the vertical.)
(A) There is no force in the rod; the equilibrium is neutral.
(B) The rod is in tension; the equilibrium is stable.
(C) The rod is in compression; the equilibrium is stable.
(D) The rod is in tension; the equilibrium is unstable.
(E) The rod is in compression; the equilibrium is unstable.
A picture may be found here http://www.aapt.org/physicsteam/2014/upload/exam1-2013-1-6-unlocked.pdf
page 6, problem 12
The Attempt at a Solution
I know that there is a force of tension because the Earth is pulling the black mass (according to diagram) down and so the rod must being pushing the white mass up to keep it in equilibrium as it rotates. I'm just having trouble about whether the equilibrium is stable or not. Any thoughts?