Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D₁ has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s⁻¹. Disc D₂ has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s⁻¹. The two discs are b

Question

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D₁ has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s⁻¹. Disc D₂ has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s⁻¹. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s⁻¹) of the system is

Accepted Answer

60. The final angular velocity is determined using the conservation of angular momentum. The moment of inertia of D₁ is I₁ = (1/2) * m₁ * r₁² = 0.04 kg·m², and for D₂, I₂ = (1/2) * m₂ * r₂² = 0.02 kg·m². The initial angular momentum is L₁ + L₂ = I₁ω₁ + I₂ω₂ = (0.04 * 50) + (0.02 * 200) = 2 + 4 = 6 kg·m²/s. Since angular momentum is conserved, the final angular velocity ω_f = (L₁ + L₂) / (I₁ + I₂) = 6 / (0.04 + 0.02) = 100 rad/s.

Solution

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