A 45 kg figure skater is spinning on the toes of her skates at 0.60 rev/s . Her

Question

A 45 kg figure skater is spinning on the toes of her skates at 0.60 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, 71 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.

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

Explanation / Answer

initial moment of inertia = moment of inertia of cylinder + 2 * moment of inertia of rods

initial moment of inertia = 0.5 * 40 * 0.1^2 + 2 * (1/3) * 2.5 * 0.71^2

initial speed = 0.60 rev /sec or 3.76991 rad / sec

final moment of inertia = 0.5 * 45 * 0.1^2

by conservation of momentum

initial momentum = final momentum

(0.5 * 40 * 0.1^2 + 2 * (1/3) * 2.5 * 0.71^2) * 3.76991 = 0.5 * 45 * 0.1^2 * v

v = 17.428 rad/sec or 2.773 rev / sec

new rotation frequency = 2.773 rev / sec

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