A thin circular ring of mass ' M ′ and radius ' R ′ is rotating about a transverse axis passing through its centre with constant angular velocity ' ω '. Two objects each of mass &#

Question

A thin circular ring of mass ' M ′ and radius ' R ′ is rotating about a transverse axis passing through its centre with constant angular velocity ' ω '. Two objects each of mass 'm' are attached gently to the opposite ends of a diameter of the ring. What is the new angular velocity?

TestHub · Accepted Answer

Initial angular momentum of the ring = I ω = M R 2 ω If the new angular velocity is ω ′ then the final angular momentum = I ′ ω ′ where I ′ = M R 2 + 2 m R 2 = ( M + 2 m ) R 2 . By law of conservation of momentum I ′ ω ′ = I ω ( M + 2 m ) R 2 ω ′ ∴ ω ′ = M + 2 m M ω ​ ​ = MR 2 ω

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