A 45 kg figure skater is spinning on the toes of her skates at 0.50 rev/s . Her

Question

A 45 kg figure skater is spinning on the toes of her skates at 0.50 rev/s . Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (40 kg , 20 cm average diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 70 cm 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.

Part A

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

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Initial moment of inertia = 0.5M1R^2 + 2*[1/12 M2L^2 + M2X^2]

= 0.5*40*0.1*0.1 + 5*(0.7*0.7/12 + 0.45*0.45) = 1.4167

Final moment of inertia = 0.5 MR^2 = 0.5*45*0.10*0.10 = 0.2250

Angular momentum is conserved

i1w1 = i2w2

w2 =w1i1/i2 = 0.50*1.4167/0.2250 = 3.1 rev/s

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