Two discs of same moment of inertia ( I ) are rotating in same sense about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities ω 1 and ω 2 . They are brought into contact face to face coinciding the axis of rotation. The expression for loss in energy during this process is

Step-by-step solution

The initial angular momentum of two discs is I 1 ω 1 + I 2 ω 2 = I ω 1 + ω 2 . The final angular momentum of system is I 1 + I 2 ω = 2 I ω From the conservation of angular momentum, ω = ω 1 + ω 2 2 . Initial kinetic energy, K E i = 1 2 I ω 1 2 + ω 2 2 and final kinetic energy, K E f = 1 2 2 I ω 1 + ω 2 2 4 Loss in kinetic energy is Δ K E = 1 2 I 1 I 2 I 1 + I 2 ω 1 - ω 2 2 = 1 2 I 2 2 I ω 1 - ω 2 2 = 1 4 I ω 1 - ω 2 2