Pulley is rotating with angular velocity ω. Pulley is sufficiently rough so that string does not slip on the pulley. Then angular momentum of system (pulley + blocks) about axle of pulley is:-

Question

G1 Physics · Accepted Answer

Each block moves with speed v=ωr, so its angular momentum about the pulley axle is mrv=mr²ω. The pulley contributes Iω. Hence L=(m₁+m₂)r²ω+Iω, which is option C.