
\sect{Gas in a centrifuge}

A cylinder of of radius ${R}$ rotates about its axis
with a constant angular velocity ${\Omega}$.  
It contains an ideal classical gas of $N$ particles 
at temperature ${T}$. Find the density distribution 
as a function of the radial distance from the axis. 
Write what is the pressure on the walls.

Note that the Hamiltonian in the rotating frame 
is ${H'\left(r,p; \Omega\right) = H\left(r,p\right) - \Omega L\left(r,p\right)}$ 
where ${L\left(r,p\right)}$ is the angular momentum. 

It is conceptually useful to realize that formally the Hamiltonian 
is the same as that of a charged particle in a magnetic field ("Coriolis force") 
plus centrifugal potential ${V\left(r\right)}$.  
Explain how this formal equivalence can be used in order 
to make a shortcut in the above calculation.

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