STANDARDPhysics-Rotational Motion
STANDARD Physics Conservation of Angular Momentum MCQ Question
Type: MCQ-conceptual-Medium
Two discs of moments of inertia I₁ and I₂ about their respective axes, rotating with angular frequencies ω₁ and ω₂ respectively, are brought into contact face to face with their axes of rotation coinciding with each other. The angular frequency of the composite disc will be
A
I₁ω₁ + I₂ω₂ / I₁ + I₂
B
I₁ω₁ + I₂ω₂ / I₁ - I₂
C
I₁ω₁ - I₂ω₂ / I₁ - I₂
D
I₁ω₁ - I₂ω₂ / I₁ + I₂
Correct Answer
Option A
Detailed Explanation
The total initial angular momentum of the two discs is Lᵢ = I₁ω₁ + I₂ω₂. When the discs are brought into contact, the moment of inertia becomes I = I₁ + I₂. Using conservation of angular momentum, Lᵢ = Lf, we find ω = (I₁ω₁ + I₂ω₂) / (I₁ + I₂).
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