A round disc of moment of inertia I _ 2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I _ 1 rotating with an angular velocity about the same axis. The final angular velocity of the combination of discs is
D. I _ 1 I _ 1 + I _ 2
Total angular momentum of the system initially \( L _ i = I _ 1 w + I _ 2 (0)= I _ 1 w \) Total angular momentum of the system finally \(L_ f = (I_ 1 +I_ 2 ) w_ 2 \) According to conservation of angular momentum i.e. \( L _ i = L _ f \) \( aligned & I _ 1 = ( I _ 1 + I _ 2 ) _ 2 \\ & _ 2 = I _ 1 I _ 1 + I _ 2 aligned \)
Related: Physics — Rotational Motion · All PYQ Banks