Two 25 kg children are sitting on a merry-go-round that is rotating at 0.10 rad/s. if one child is 1.0 m from the center and the other is 1.5 m from the center, what is their combined angular momentum?

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