Moment Of Inertia

The system described involves two discs with different moments of inertia and angular velocities. To find the angular frequency of the composite disc, we apply the principle of conservation of angular momentum. The total angular momentum of the system before the discs are combined is the sum of the individual angular momenta of the discs. The angular momentum of an object is given by: where is the moment of inertia and is the angular velocity. - For the first disc: - For the second disc: The total angular momentum of the system is: Since angular momentum is conserved, the total angular momentum after the discs are combined is equal to the total angular momentum before. The combined moment of inertia is: Thus, the final angular velocity is: Therefore, the angular frequency of the composite disc is 8 rad/s, so the correct answer is (C).