Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc $D_1 $ has 2 kg mass and 0.2 m radius and initial angular velocity of $ 50\, rad \,s^{-1}.$ Disc $ D_2 $ has 4 kg mass, 0.1 m radius and initial angular velocity of $ 200\, rad\, s^{-1} $. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad $ s^{-1}$ ) of the system is