The angular speed of the merry-go-round is
ω = 0.10 rad/s
The angular moment of inertia of a mass, m, at a radius, r, from the center of the wheel is
I = mr²
Therefore, the angular moment of inertia for the children are
I₁ = (25 kg)*(1.0 m)² = 25 kg-m²
I₂ = (25 kg)*(1.5 m)² = 56.25 kg-m²
The combined angular momentum is
ω(I₁ + I₂) = (0.10 rad/s)*(25 + 56.25 kg-m²)
= 8.125 (kg-m²)/s
Answer: 8.125 (kg-m²)/s
