A 45 kg figure skater is spinning on the toes of her skates at 0.80 rev/s . Her

Question

A 45 kg figure skater is spinning on the toes of her skates at 0.80 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, 67 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?

not 1.4 rev/s

Explanation / Answer

Given,

M = 40 kg, m = 2.5 kg, R = D/2 = 0.1 m

Initial Moment of inertia, I1= 0.5 MR2 + 2 x[(1/12)mL2 + m(R+L/2)2]

I1 = (1/2) x 40 x 0.12 + 2[(1/12) x 2.5 x 0.672 + 2.5(0.1+0.67/2)2]

I1=1.33 Kg-m2

Final Moment of inertia,

I2 = 0.5 MR2

I2 = 0.5 x 45 x 0.12 = 0.225 Kg-m^2

By principle of conservation of angular momentum,

I11 = I22

1.33 x 0.80 = 0.225 x 2

2 = 4.73 rev/s

(Please rate my answer if you find it helpful, good luck...)

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