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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? rpm

Explanation / 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