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 9.0 kg . When outstretched, they span 1.8 m ; when wrapped, they form a cylinder of radius 24 cm . The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.40kgm2.

If his original angular speed is 0.50 rev/s , what is his final angular speed?

Express your answer using two significant figures.

Explanation / Answer

from the conservation of angualr momnetum

Li = Lf

Ii wi = If wf

Io + 1/12 mr^2 * wi =( Io + mr^2) wf

wf = Io + 1/12 mr^2 * wi /Io+ mr^2

= 0.40+ (1/12) ( 9) ( 1.8 m)^2 * 0.50 rev/s /(0.40)+ 9 kg ( 0.24 m)^2

=1.75 rev/s

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