A 45 kg figure skater is spinning on the toes of her skates at 1.3 rev/s . Her a

Question

A 45 kg figure skater is spinning on the toes of her skates at 1.3 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 cmaverage diameter, 160 cm tall) plus two rod-like arms (2.5 kg each, 69 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.

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

Explanation / Answer

Iarms = moment of inertai of each arm = (1/3) m L2 = (1/3) = (1/3) (2.5) (0.69)2 = 0.39675 kgm2

Itorso = moment of inertai of cylindrical torso = (0.5) M r2 = (0.5) (40) (0.10)2 = 0.2 kgm2

Total initial moment of inertia = Ii = Itorso + 2 Iarms = 0.2 + 2 (0.39675) = 0.9935 kgm2

Wi = initial angular speed = 1.3 x 3.14 x 2 rad/s = 8.164 rad/s

If = final moment of inertia = (0.5) M' r2 = (0.5) (45) (0.10)2 = 0.225 kgm2

Wf = final angular speed

using conservation of angular momentum

Ii Wi = If Wf

(0.9935) (8.164) = (0.225) Wf

Wf = 36.1 rad/s = 36.1/(2 x 3.14) = 5.75 rev/s

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