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## Homework Statement

A cylinder with radius R spins around its axis with an angular speed ω. On its inner surface there lies a small block; the coefficient of friction between the block and the inner sur- face of the cylinder is μ. Find the values of ω for which the block does not slip (stays still with respect to the cylinder). Consider the cases where (a) the axis of the cylinder is hori- zontal; (b) the axis is inclined by angle α with respect to the horizon.

## Homework Equations

## The Attempt at a Solution

I tried to figure out which are the forces applied to the block in the non inertial frame of the cylinder. There is ##m \vec{g} ##, the centrifugal force ##\vec{F_{c}} = m \omega^2 \vec{R}##, the normal reaction ## \vec{N} ## and the frictional force ## \vec{F_{s}}= \vec{N} \mu ##. If the block is at rest the sum ## m \vec{g} + \vec{F_{c}} + \vec{N} + \vec{F_{s}} = 0 ##.

Considering only case (a) of the problem, I don't know how to work with this equation in a three dimension, because my first solution where that ## \omega = \sqrt{ \frac{\mu g}{R}} ## but I think it's correct in a two-dimensional geometry. Any help or reference to see?