11. -12 points FRKestenCP1 8.P.103. My Notes On average both arms and hands toge
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11. -12 points FRKestenCP1 8.P.103. My Notes On average both arms and hands together account for 13% of a person's mass while the head is 7.0%, and the trunk and egs account or 80 can model a spinning skater with his arms outstretched as a vertical cylinder (head trunk +legs) with two solid uniform rods (arms + hands) extended horizontally. Suppose a 64-kg skater is 1.5 m tall, has arms that are each 62 cm long (including the hands), and a trunk that can be modeled as being 38 cm in diameter. If the skater is initially spinning at 61 rpm with his arms outstretched, what will his angular velocity be (in rpm) when he pulls in his arms until they are at his sides parallel to his trunk? rpm Supporting Materials Pcast eBookExplanation / Answer
Mtorso = mass of trunk + mass of legs + head = 0.8M + 0.07M = 0.87 M = 0.87*64 = 55.68 kg
mass of each arm = Marm = 6.5% = 0.065 M = 0.065*64 = 4.16 kg
initial moment of inertia
Iinitial = (1/2)*Mtorso*r^2 + 2*( (1/12)*Marm*L^2 + Marm*(r+L/2)^2 )
Iinitial = (1/2)*55.6*0.19^2 + 2*( (1/12)*4.16*0.62^2 + 4.16*(0.19 + 0.62/2)^2) = 3.35 kg m^2
initial angular momentum Li = Iinitial *wi
final moment of inertia
Ifinal = (1/2)*Mtorso*r^2 + 2*Marm*r^2
Ifinal = (1/2)*55.6*0.19^2 + 2*4.16*0.19^2 = 1.3 kg m^2
final angular momentum Lf = Ifinal *wf
from momentum conservation
Lf = Li
1.3*w2 = 3.35*61
w2 = 157.2 rpm
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