# Very fast spinning

A boy is spinning on a chair and holding a paper bag so that it is horizontal, and perpendicular to the axis of the rotation. What should be the angular velocity of the boy in radians/second so that the bottom of the bag breaks?

Details and assumptions

• Assume paper breaks at an overpressure of $$1.2~\mbox{atm}$$.
• The molecular mass of the air is $$29~\mbox{g/mol}$$.
• The boy's arm is $$L = 70~\mbox{cm}$$ long.
• When horizontal, the bag has a shape of a cylinder of length $$30~\mbox{cm}$$.
• Outside pressure is $$1~\mbox{atm}$$ and temperature $$25^\circ \mbox{C}$$.
• Assume that the boy won't get sick no matter how fast he is spinning. Hint: he whizzes around.
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