Question

# Luc, who is 1.80 m tall and weighs 950 N, is standing at the center of...

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?

m1 = 1500 / 10 = 150 kg

m2 = 950 / 10 = 95 kg

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

Ii = 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

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

Ii wi = If wf

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

= 3.3 * (60 / 2 pi)

= 31.5 rpm

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