Halliday, Resnick & Walker — Rolling, Torque, and Angular Momentum: Problem 56

56 In a long jump, an athlete leaves the ground with an initial angular momentum that tends to rotate her body forward, threatening to ruin her landing. To counter this tendency, she rotates her outstretched arms to “take up” the angular momentum (Fig. 11-18). In 0.700 s, one arm sweeps through 0.500 rev and the other arm sweeps through 1.000 rev. Treat each arm as a thin rod of mass 4.0 kg and length 0.60 m, rotating around one end. In the athlete’s reference frame, what is the magnitude of the total angular momentum of the arms around the common rotation axis through the shoulders?