Two discs have moments of intertia I 1 and I 2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, ω 1 and ω 2 respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by:

Step-by-step solution

Angular momentum conservation I 1 ω 1 + I 2 ω 2 = I 1 + I 2 ω ω = I 1 ω 1 + I 2 ω 2 I 1 + I 2 Loss = 1 2 I 1 ω 1 2 + 1 2 I 2 ω 2 2 - 1 2 I 1 + I 2 ω 2 = 1 2 I 1 ω 1 2 + 1 2 I 2 ω 2 2 - 1 2 I 1 + I 2 I 1 ω 1 + I 2 ω 2 I 1 + I 2 2 = 1 2 I 1 I 2 I 1 + I 2 ω 1 - ω 2 2 E i - E f = I 1 I 2 ω 1 - ω 2 2 2 I 1 + I 2