A 45 kg figure skater is spinning on the toes of her skates at 1.0 rev/s. Her ar

Question

A 45 kg figure skater is spinning on the toes of her skates at 1.0 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, 66 cm) 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

radius = 20 cm / 2 = 10 cm

radius = 0.1 m, m = 40 kg

The moment of inertia for a cylinder I = m * r2 / 2 = 40 * 0.12 / 2 = 0.2 kg.m2

mass = 2.5 kg, length = 66 cm = 0.66 m

I = m L2 / 12 = 2.5 * 0.662 / 12 = 0.091 kg.m2

distance can be expressed as half the length of her arm and the radius of her body

d = 0.66 / 2 + 0.1 = 0.43 m

From the parallel axis theoremI = Icenter + m d2

= 0.091 + (2.5 * 0.432) = 0.553 kg.m2

I = Ibody + 2 * Iarms = 0.2 + (2 * 0.553) = 1.31 kg.m2

From the equation for angular momentum

Li = I * w = 1.306 * 1 rev/s

radius = 0.1 m, m = 45 kg

I = m * r2 / 2 = 45 * 0.12 / 2 = 0.225 kg.m2

Lfinal = Li

I * w = 1.31

w = 1.31 / 0.225 = 5.8 rev/s

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