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
Iinitial*Wintial = IFinal*Wfinal
1.279*0.6 = 0.225*Wfinal
W final = 3.4 rad/s
Conclusion
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