A diver with a moment of inertia of 6.0 kg-m^2 about an axis...

According to the principle of conservation of angular momentum, if no external torque acts on a system, its total angular momentum remains constant.

Initial angular momentum $L_1 = I_1 \omega_1$

Final angular momentum $L_2 = I_2 \omega_2$

Equating the initial and final angular momentum:

$I_1 \omega_1 = I_2 \omega_2$

Substituting the given values:

$6.0 \times 2 = 5.0 \times \omega_2$

$\omega_2 = \dfrac{12.0}{5.0} = 2.4 \text{ rad/s}$