By the conservation of angular momentum, I₁ω₁ = I₂ω₂. Initial moment of inertia I₁ = Mr². Final moment of inertia I₂ = Mr² + 2mr² = (M+2m)r². So, Mr²ω = (M+2m)r²ω'. Solving for ω' gives ωM / (M+2m).