Classical Mechanics Level 5

During a jump to his partner, an aerialist is to make a quadruple somersault lasting a time $$t = 1.87 s$$. For the first and last quarter-revolution, he is in the extended orientation shown in the figure, with rotational inertia $$I_{1} = 19.9 kgm^{2}$$ around his center of mass (the dot). During the rest of the flight he is in a tight tuck, with rotational inertia $$I_{2} = 3.93 kgm^{2}$$ What must be his angular speed $$\omega_{2}$$ in $$rev/s$$ around his centre of mass during the tuck?

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