A uniform solid disc of mass M and radius R is rotating freely with an angular velocity ₀ about a vertical axis passing through its center. Two identical lumps of putty, each of mass m , are dropped gently onto the disc. They stick to the disc at a distance of R 2 from the axis of rotation, on opposite sides. The new angular velocity of the system is

Step-by-step solution

Since the lumps of putty are dropped gently, there is no external torque acting on the system about the axis of rotation. Therefore, angular momentum is conserved. Initial moment of inertia of the solid disc is I_i = 1 2 MR^2 The two lumps of putty are placed at a distance of R 2 from the axis. Their combined moment of inertia is I_ putty = 2 m ( R 2 )^2 = 1 2 mR^2 Final moment of inertia of the system is I_f = I_i + I_ putty = 1 2 MR^2 + 1 2 mR^2 = 1 2 (M+m)R^2 By conservation of angular momentum, I_i ₀ = I_f _f 1