The outstretched hands and arms of a figure skater preparing

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 7.0 kg . When outstretched, they span 1.6 m ; when wrapped, they form a cylinder of radius 26 cm . The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.40kgm2.

A. If his original angular speed is 0.30 rev/s , what is his final angular speed? Express your answer using two significant figures.

Solution

moment of inertia of rod about center axis = mL^2 / 12

initial:

Ii = 0.40 + (9 x 1.6^2 / 12) = 2.32 kg m^2

wi = 0.40 rev/s

finally :

If = 0.40 + ( 9 x 0.24^2) = 0.92 kg m^2

using angular momentum conservation,

Ii wi = If wf

2.32 x 0.40 = 0.92 x wf

wf = 1.01 rev / s