Two discs of moment of inertia I 1 = 4 kg m 2 and I 2 = 2 kg m 2 about their central axes & normal to their planes, rotating with angular speeds 10 rad s - 1 & 4 rad s - 1 respectively are brought into contact face to face with their axe of rotation coincident. The loss in kinetic energy of the system in the process is _________ J .

Step-by-step solution

Applying conservation of angular momentum, we get I 1 ω 1 + I 2 ω 2 = I 1 + I 2 ω 0 ⇒ 4 × 10 + 2 × 4 = 4 + 2 ω 0 ⇒ ω 0 = 8 rad s - 1 Now, initial rotational kinetic energy is E 1 = 1 2 I 1 ω 1 2 + 1 2 I 2 ω 2 2 = 216 J and final rotational kinetic energy is E 2 = 1 2 I 1 + I 2 ω 0 2 = 192 J Required, energy loss Δ E = E 1 - E 2 = 24 J