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?
m_{1} = 1500 / 10 = 150 kg
m_{2} = 950 / 10 = 95 kg
w_{i} = 31 * 2 pi / 60 = 3.24 rad/s
I_{i} = 1/2 m_{1} r_{1}^{2} + 1/2 m_{2} r_{2}^{2} + 2 m_{3} r_{3}^{2} = (1/2 * 150 * 2^{2}) + (1/2 * 95 * 0.2^{2}) + (2 * 4 * 0.85^{2}) = 307.7
I_{f} = 1/2 m_{1} r_{1}^{2} + 1/2 m_{2} r_{2}^{2} = (1/2 * 150 * 2^{2}) + (1/2 * 95 * 0.2^{2}) = 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
Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of...
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