Ann, Sam and you take a trip to the orbiting International Space Station, bringing along a hula hoop that is 1.02 m in diameter (= 2R) and has a mass Mh = 2.0 kg. You are watching from a viewport while Sam and Ann go outside for a (space) walk. You see both Sam and Ann motionless in space a distance D = 23.6 m apart and oriented in the same direction as each other, parallel head to toe along a line joining their centers of mass. Ann is holding the hula hoop motionless, centered on her body, but decides to throw it ‘up’ to Sam, giving the hula hoop a spin in the process. You observe the hula hoop moving between Ann and Sam with a translational speed vh = 3.9 m/s and spin of frequency fh = 2.5 revolutions/sec. Sam catches the hula hoop and holds it as shown. Sam has a mass (including spacesuit) Ms = 90 kg and a moment of inertia about his axis Is = 0.65 kg-m2. Ann has a mass (also including space suit) 2

MA = 65 kg and a moment of inertia about her axis of IA = 0.55 kg-m .
After Sam catches the hula hoop, you see both Sam and Anne spinning and moving away from each other. Calculate their translational velocities vA and vS and the frequencies fS and fA at which they are spinning. Solve for each quantity first in terms of symbols; don’t plug in the numerical values you are provided until the last possible step.

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Ann, Sam and you take a trip to the orbiting International Space Station, bringing along a hula hoop that is 1.02 m in diameter (= 2R) and has a mass Mh = 2.0 kg. You are watching from a viewport while Sam and Ann go outside for a (space) walk. You see both Sam and Ann motionless in space a distance D = 23.6 m apart and oriented in the same direction as each other, parallel head to toe along a line joining their centers of mass. Ann is holding the hula hoop motionless, centered on her body, but decides to throw it ‘up’ to Sam, giving the hula hoop a spin in the process. You observe the hula hoop moving between Ann and Sam with a translational speed vh = 3.9 m/s and spin of frequency fh = 2.5 revolutions/sec. Sam catches the hula hoop and holds it as shown. Sam has a mass (including spacesuit) Ms = 90 kg and a moment of inertia about his axis Is = 0.65 kg-m2. Ann has a mass (also including space suit) 2
MA = 65 kg and a moment of inertia about her axis of IA = 0.55 kg-m .
After Sam catches the hula hoop, you see both Sam and Anne spinning and moving away from each other. Calculate their translational velocities vA and vS and the frequencies fS and fA at which they are spinning. Solve for each quantity first in terms of symbols; don’t plug in the numerical values you are provided until the last possible step.