on average both arms and hands together account for 13% of a person\'s mass whil
ID: 1781329 • Letter: O
Question
on average both arms and hands together account for 13% of a person's mass while the ea is 7.0% and the trunk and legs account or e 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 67-kg skater is 1.6 m tall, has arms that are each 61 cm long (including the hands), and a trunk that can be modeled as being 33 cm in diameter. If the skater is initially spinning at 71 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? rpmExplanation / Answer
M = mass of trunk = 0.8 x 67 = 53.6 kg
R = radius of trunk = 0.33/2 = 0.165 m
Itrunk = moment of inertia of trunk = (0.5) MR2 = (0.5) (53.6) (0.165)2 = 0.73 kgm2
Iarms = mL2/3 = (0.13 x 67) (0.61)2/3 = 1.1 kgm2
Ii = initial moment of inertia = Itrunk + Iarms = 0.73 + 1.1 = 1.83 kgm2
If = final moment of inertia = Itrunk = 0.73 kgm2
wi = initial angular velocity = 71 rpm
wf = final angular velocity = ?
using conservation of angular momentum
Ii wi = If wf
(1.83) (71) = (0.73) wf
wf = 178 rpm
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