A diver can change his rotational inertia by drawing his arms and legs close to his body in the tuck position. After he leaves the diving board (with some unknown angular velocity), he pulls himself into a ball as closely as possible and makes 2.16 complete rotations in 1.31 s. If his rotational inertia decreases by a factor of 2.90 when he goes from the straight to the tuck position, what was his angular velocity when he left the diving board?

Answer 1

The thing that stays constant here is the angular momentum which is angular velocity (omega) times rotational inertia (I)

so write:

angular velocity before times rotational inertia before equals angular velocity after times rotational inertia after.
By the way angular velocity is usually expressed in radians per second so you will have to get that from the "after" data of 2.16 rotations in 1.31 seconds.