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 atm 1.2~\mbox{atm}.
  • The molecular mass of the air is 29 g/mol 29~\mbox{g/mol}.
  • The boy's arm is L=70 cmL = 70~\mbox{cm} long.
  • When horizontal, the bag has a shape of a cylinder of length 30 cm30~\mbox{cm}.
  • Outside pressure is 1 atm1~\mbox{atm} and temperature 25C25^\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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