A 45kg figure skater is spinning on the toes of her skates at 0.70rev/s . Her ar

Question

A 45kg figure skater is spinning on the toes of her skates at 0.70rev/s . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40kg , 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 66cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20-cm-diameter, 200-cm-tall cylinder.

What is her new rotation frequency, in revolutions per second?

Explanation / Answer

R=D/2 =0.1 m

Initial Moment of inertia

I1=(1/2)*M*R2 +2*[(1/12)*m*L2+m*(R+L/2)^2]

I1=(1/2)*40*0.12+2[(1/12)*2.5*0.662 +2.5*(0.1+0.66/2)2]

I1=1.306 Kg-m2

Final Moment of inertai

I2=(1/2)*M*R2

I2=(1/2)*45*0.1^2 =0.225 Kg-m^2

By conservation of angular momentum

I1*W1=I2*W2

1.306*0.7=0.225*W2

W2=4.06 rev/s

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