E216: Density of a gas inside a rotating box
A cylinder of radius R and height H rotates about its axis with a constant angular velocity
W. It contains an ideal classical gas at temperature T. Find the density distribution as
function of the distance r from the axis. Note that the Hamiltonian in the rotating frame
is H'(p,q; W) = H(p,q) - WL(p,q) where L(p,q) is the angular momentum. It is
conceptually useful to realize that it is formally the Hamiltonian of a charged particle in a
magnetic field (="Coriolis force") plus centrifugal potential V(r). Explain how this
formal equivalence can be used in order to make a "shortcut" in the above calculation.