Mass Sliding Down a Rotating Inclined Tube with Friction
A particle of mass slides from the center of a rotating tube at an angle with a vertical bar. The angular velocity and the friction coefficient determine the direction in which the particle slides.
The equation for is
with the normal force
The conditions for incipient outward and inward motion are, respectively,
 D. T. Greenwood, Advanced Dynamics, Cambridge, UK: Cambridge University Press, 2003.