The outstretched hands and arms of a figure skater preparing for a spin can be c

Question

The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center (Figure 1) . When his hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass 8.0 kg . When outstretched, they span 1.9 m ; when wrapped, they form a cylinder of radius 23 cm . The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.40kg?m2.

If his original angular speed is 0.40 rev/s , what is his final angular speed?

Explanation / Answer

Use law of conservation of momentum,

Li=Lf

I1w1 = I2w2

(Ibody+ Istretched hands)w1 = (Ibody+ Ipulled hands)w2

(Ibody+ Ipoint mass )w1 = (Ibody+ Icylinder)w2

(Ibody+ mr12 )w1 = (Ibody+ mr22) )w2

(0.40+(8*1.9^2))*0.40 = (0.40+(8*0.0023^2)w2      => w2= 267.3 rad/s

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