A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω. If another disc of same dimensions but of mass M/2 is placed gently on the first disc co-axially, then the new angular velocity of the system is:
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Question

A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω. If another disc of same dimensions but of mass M/2 is placed gently on the first disc co-axially, then the new angular velocity of the system is:

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G1 Physics · Accepted Answer

Angular momentum is conserved. Moment of inertia of first disc: I₁ = ½MR² Moment of inertia of second disc: I₂ = ½(M/2)R² = ¼MR² Initially: Lᵢ = I₁ω Finally: L(final) = (I₁ + I₂)ω' Therefore: ½MR²ω = (½MR² + ¼MR²)ω' ½ω = ¾ω' Hence: ω' = 2ω/3