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 7.0 kg . When outstretched, they span 1.8 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.

Part A

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

2 =

Explanation / Answer

Now using law of conservation of angular momentum

L1 = L2

But L = I*w

I is the moment of inertia

w is the angular speed

then

(I+I1)*w1 = (I+I2)*w2

I1 = (1/2)*M*L^2 = (1/12)*7*1.8^2 = 1.89 kg-m^2

I2 = m*r^2 = 7*0.26^2 = 0.4732 kg-m^2

I = 0.4 kg*m^2

then

(0.4+1.89)*0.3 = (0.4+0.4732)*w2

w2 = 0.786 rev/sec = 0.786*2*3.142 = 4.94 rad/s

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