The initial angular velocity of a circular disc of mass M is ω₁. Then two small spheres of mass m are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

Question

Accepted Answer

(3) (M/(M+4m))ω₁. The spheres are attached gently, so no external torque acts and angular momentum about the axis is conserved. Disc alone: Iᵢ=(MR²)/2. Each sphere sits on the edge, a distance R from the axis, adding mR²: I_f=(MR²)/2+2mR². (MR²)/2ω₁=((MR²)/2+2mR²)ω₂. Divide through by (R²)/2: Mω₁=(M+4m)ω₂. ω₂=(M/(M+4m))ω₁. The 4 is the whole point: it comes from the disc's 1/2, and it is what separates this from the same question asked about a ring.

The initial angular velocity of a circular disc of mass M is ω₁. Then two small spheres of mass m are attached gently to two diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

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