A 46.4 kg figure skater is spinning on the toes of her skates at 1.21 rpm. Her a

Question

A 46.4 kg figure skater is spinning on the toes of her skates at 1.21 rpm. Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (41.7 kg, 19.5 cm average diameter, 153.0 cm tall) plus two rod-like arms (2.34 kg each, 76.5 cm long) that each rotate about an axis through the inner end of the rod. The skater then raises her arms straight above her head, where she appears to be a 46.4 kg, 19.5 cm diameter, 185.0 cm tall cylinder. What is her new rotation frequency, in radians per second?

Explanation / Answer

= 1.21 rpm = 1.21 x 2 / 60 = 0.127 rad/s

Ii = 41.7 x 0.09752 /2 + 2 x 2.34 x 0.7652 /3   = 1.111 kg-m2   

If = 46.4 x 0.09752 /2 = 0.221 kg-m2  

using angular momntum conservation,

1.111 x 0.127 = 0.221 x

= 0.638 rad/s

= 2f

f = 0.638 / 2 = 0.1016 rev/s = 6.10 rpm

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