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## Homework Statement

A small solid cylinder of radius r lies inside a large tube of internal radius R. Show that the angular velocity of the small tube $$\omega$$ is related to $$ \psi $$, the angle between the centre of mass of the solid cylinder, the centre of the large tube and the vertical by;

$$\omega = \dfrac{R-r}{r} \dfrac{d\psi}{dt}$$

The find the period of oscillation of the small cylinder about its equilibrium position.

## Homework Equations

See below.

## The Attempt at a Solution

I cannot quite imagine the whole setup I assumed that the objects should touch otherwise the angular velocities of the cylinder and the pipe should not have any relation. I tried to apply the conservation of angular momentum, by assuming that we start turning one cylinder and this one then exert torque on the other cylinder.... I did not work.

For the second part I assume I would want to use the energy method, but being able to visualise the problem clarifying the set up I am stuck.

Could someone please explain the setup to me and maybe give some hints.