**A 45 kg figure skater is spinning on the toes of her skates at 0.60 rev/s**

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## Question “A 45 kg figure skater is spinning on the toes of her skates at 0.60 rev/s”

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, 65 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?

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

## Answer

Initial moment of inertia = Moment of Inertia for Person (IC)+ Moment Of Inertia for His Arms (IA). Moment of inertia for Personas Cylinder (IC = (1/2).MR2 = (1/2),*40*(0.11)2 = 0.2kg-m2

Where M is the mass of a person as cylinder = 40kg

R = radius of person as a cylinder = 10 cm = 0.01 m

Moment of inertia for arms

I _{I}= I _{} _{Enter} + m*x ^{3}

2.25*2 = 5 Kg = m = the mass of the arms

where x is the distance between center of arms (x) and center of cylinders (L/2)+R = 32.25+10 = 42.5 cm

Where L is the length of your arms = 65 cm

= mL2/12) +(mx2) = (5*0.652/12) +(5*0.4252) = 1.079 kg-m2

Now, the system’s total moment of inertia

I _{initial} = _{C} + _{A} = 1.27 kg-m ^{2.}

The system is now in its final moment of inertia

I _{final} =(1/2)(m+M),R ^{2} = 45*(0) ^{2} = 0.225kg-m ^{2}

Use the angular Conservation to momentum

I_{initial}*W_{intial } = I_{Final}*W_{final}

1.279*0.6 = 0.225*W_{final}

W _{final} = 3.4 rad/s

## Conclusion

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