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Two discs of moments of inertia I₀₁ and I₀₂ are rotating with angular velocities ω₁ and ω₂ respectively. If they are brought into contact, what is the loss in kinetic energy?

1. Loss in K.E. = 1/4 (ω₁ - ω₂)²
2. Loss in K.E. = 1/2 (ω₁ - ω₂)²
3. Loss in K.E. = (ω₁ - ω₂)²
4. Loss in K.E. = 1/8 (ω₁ - ω₂)²

Correct answer: Loss in K.E. = 1/2 (ω₁ - ω₂)²

Solution

When the two discs are brought into contact, they will eventually rotate with a common angular velocity due to conservation of angular momentum. The loss in kinetic energy is given by the difference between the initial and final rotational kinetic energies. After solving, the loss in kinetic energy is found to be proportional to 1/2 (ω₁ - ω₂)².

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