A 45 kg figure skater is spinning on the toes of her skates at 0.90 rev/s . Her

Q: A 45 kg figure skater is spinning on the toes of her skates at 0.90 rev/s . Her

given wi = 0.9 rev/s Initial moment of inertia, I1 = 0.5*M*r^2 + 2*m*L^2/3 = 0.5*40*0.1^2 + 2*2.5*0.62^2/3 = 0.8407 kg.m^2 final moment of inertia, If = 0.5*(M + 2*m)*r^2 = 0.5*45*0.1^2 = 0.225 kg.m^2 wf = ? Apply conservation of angular momentum If*wf = Ii*wi wf = Ii*wi/If = 0.8407*0.9/0.225 = 3.4 rev/s

ID: 1517228 • Letter: A

Question

A 45 kg figure skater is spinning on the toes of her skates at 0.90 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, 62 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?

Express your answer to two significant figures and include the appropriate units.

rev/s

Explanation / Answer

given
wi = 0.9 rev/s

Initial moment of inertia, I1 = 0.5*M*r^2 + 2*m*L^2/3

= 0.5*40*0.1^2 + 2*2.5*0.62^2/3

= 0.8407 kg.m^2

final moment of inertia, If = 0.5*(M + 2*m)*r^2

= 0.5*45*0.1^2

= 0.225 kg.m^2

wf = ?

Apply conservation of angular momentum

If*wf = Ii*wi

wf = Ii*wi/If

= 0.8407*0.9/0.225

= 3.4 rev/s <<<<<------------Answer

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A 45 kg figure skater is spinning on the toes of her skates at 0.90 rev/s . Her

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