A horizontal cylinder closed from one end is rotated with a constant angular velocity \( \omega ...

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A horizontal cylinder closed from one end is rotated with a constant angular velocity \( \omega \) about a vertical axis passing through the open end of the cylinder. The outside air pressure is equal to \( p_{0} \), the temperature to \( T \), and the molar mass of air to \( M \). Find the air pressure as a function of the distance \( r \) from the rotation axis. The molar mass is assumed to be independent of \( r \).
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