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.

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

Explanation / Answer

1st convert rev/s to rad/s. One revolution = 2*pi radians

0.6 rev/s = 0.6 * 2pi = 1.2 pi rad/s

This is a conservation of angular momentum problem

For a solid cylinder, I = m * r^2, r = 0.1 m

For a solid cylinder, I = 40 * 0.1^2 = 0.4

Angular momentum = 0.4 * (1.2pi)^2 = 0.576 * pi^2

This is the angular momentum of her torso.

For her arms, m = 5 kg , and r = 0.5 * 0.71 = 0.355

I = 5 * 0.355^2 = 0.63

Angular momentum = 0.63 * (1.2*pi)^2 = 0.9072 * pi^2

This is the angular momentum of her arms.

Total initial momentum = (0.9072+0.576) * pi^2 = 1.4832 * pi^2

. 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. r = 0.1m

I = 45 * 0.1^2 = 0.45

Final momentum = 0.45 * wf^2

0.45 * wf^2 = 1.4832 * pi^2

wf^2 = 1.4832 * pi^2 / 0.45 = 3.296 * pi^2

wf = sqrt(3.296 * pi^2) = 5.70 rad/s

Rev/s = wf / 2pi

Rev/s = sqrt(3.296 * pi^2) / 2pi = 0.9077

The answer is approximately 0.9077 rev/s.

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