# 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