11.3 Exercise 11

A diver off the high board imparts an initial rotation with their body fully extended before going into a tuck and executing three back somersaults before hitting the water. If their moment of inertia before the tuck is $16.9 \text{kg} \cdot \text{m}^{2}$ and after the tuck during the somersaults is $4.2 \text{kg} \cdot \text{m}^{2}$, what rotation rate must the diver impart to their body directly off the board and before the tuck if they take 1.4 s to execute the somersaults before hitting the water?