Gummed up hula-hoop

A gumball of mass \(m\) traveling with velocity \(v_0\) in the \(\hat{x}\) direction collides tangentially with a stationary hula-hoop of mass \(M\) of radius \(R\) (lying in the xy plane) and sticks. What is the angular frequency of the hoop and bead conglomerate (in milliradian/s) after the collision?

Details and assumptions

  • The entire system is in a space that has no gravitational forces.
  • \(M\) = 2 kg
  • \(m\) = 30 g
  • \(R\) = 0.2 m
  • \(v_0\) = 1 m/s
  • Express your answer to the nearest whole number

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