Very fast spinning

Classical Mechanics Level 5

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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