Walker, Halliday & Resnick — Rolling, Torque, and Angular Momentum: Problem 62

62 During a jump to his partner, an aerialist is to make a quadruple somersault lasting a time $t = 1.87\text{ s}$. For the first and last quarter-revolution, he is in the extended orientation shown in Fig. 11-50, with rotational inertia $I_1 = 19.9\text{ kg}\cdot\text{m}^2$ around his center of mass (the dot). During the rest of the flight he is in a tight tuck, with rotational inertia $I_2 = 4.17\text{ kg}\cdot\text{m}^2$. What must be his angular speed $\omega_2$ around his center of mass during the tuck?