Question

Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of a playground merry-go-round with his arms extended, holding a 4.0 kg dumbbell in each hand. The merry-go-round can be modeled as a 4.0-m-diameter disk with a weight of 1500 N. Luc's body can be modeled as a uniform 40-cm-diameter cylinder with massless arms extending to hands that are 85 cm from his center. The merry-go-round is coasting at a steady 31 rpm when Luc brings his hands in to his chest.

Afterward, what is the angular velocity, in rpm, of the merry-go-round?

Answer 1

m₁ = 1500 / 10 = 150 kg

m₂ = 950 / 10 = 95 kg

w_i = 31 * 2 pi / 60 = 3.24 rad/s

I_i = 1/2 m₁ r₁² + 1/2 m₂ r₂² + 2 m₃ r₃² = (1/2 * 150 * 2²) + (1/2 * 95 * 0.2²) + (2 * 4 * 0.85²) = 307.7

I_f = 1/2 m₁ r₁² + 1/2 m₂ r₂² = (1/2 * 150 * 2²) + (1/2 * 95 * 0.2²) = 301.9

I_i w_i = I_f w_f

w_f = 3.24 * 307.7 / 301.9 = 3.3 rad/s

= 3.3 * (60 / 2 pi)

= 31.5 rpm