A 1.80 m radius playground merry-go-round has a mass of 120 kg and is rotating with an angular velocity of 0.330 rev/s. what is its angular velocity, in rev/s, after a 27.5 kg child gets onto it by grabbing its outer edge? the child is initially at rest.
Solution. Initial angular velocity ωi = 0.330 × 2π rad/sec = 2.0737 rad/sec The initial moment of inertia li = 0.5×M×r² = 0.5 × 120 × 1.8² = 194.4 kgm² But the angular momentum is given by the product of moment of inertia and the angular velocity. = li × ωi = 2.0737 × 194.4 = 403.13 kg.m²/s which is constant Child moment of inertia (point mass) = m × r² = 27.5 × 1.8² = 27.5 × 3.24 = 89.1 kgm² Thus, the final moment of inertia if = 194.4 + 89.1 = 283.5 kgm² Therefore; the final speed: =403.13/ 283.5 = 1.422 rad/sec This is equivalent to; 1.422/2π = 0.2263 rev/s
