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### Physic Wiki

The purpose of this wiki is to provide physics graduate students and other scientists with peer-reviewed solutions to the types of problems that can be found on PhD qualifying exams. The articles consist of graduate-level problems from public problem banks. Public problem banks are often compiled by various university physics departments and include questions that they have given on previous PhD qualifying/prelim exams. The community can submit problems, search for problems, and post or correct solutions to these problems.

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### Featured Problem

#### Rotating tube 12/27/2009 with solution (ws)

A particle of mass m is placed in a smooth uniform tube of mass M and length l.  The tube is free to rotate about its center in a vertical plane.  The system is started from rest with the tube horizontal and the particle a distance $r_0$ from the center of the tube.

For what length of the tube will the particle leave the tube when $\dot{\theta}=\omega$ is a maximum and $\theta=\theta_m$?  Your answer should be in terms of $\omega$ and $\theta_m$.