  The behaviour of a quantum rod, pivoted at its lower end on an impenetrable
floor and restricted to moving in the vertical plane under the gravitational
potential is studied analytically under the approximation that the rod is
initially localised to a small-enough neighbourhood around the point of
classical unstable equilibrium. It is shown that the rod evolves out of this
neighbourhood. The time required for this to happen, i.e., the tipping time is
calculated using the semi-classical path integral. It is shown that equilibrium
is recovered in the classical limit, and that our calculations are consistent
with the uncertainty principle.
