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

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

radius R = Diameter/2 = 0.2/2 =0.1 m Initial Moment of inertia, MOI of cylinder + MOI of rod so Inet = 1/2)*M*R2 +2*[(1/12)*m*L2+m*(R+L/2)^2] I1=(1/2)*40*0.12+2* (1/12)*2.5*0.66^2 +2.5*(0.1+0.66/2)^2] I1=1.306 Kg m^2 now Final Moment of inertia, I2=(1/2)*M*R^2 I2=(1/2)*45*0.1^2 =0.225 Kg-m^2 By conservation of angular momentum , L1 = L2 i,e I1 W1 = I2 W2 1.306*0.8 = = 0.225*W2 W2=4.64 rev/s

ID: 1459178 • Letter: A

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, 66 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.

a) What is her new rotation frequency, in revolutions per second?

Explanation / Answer

radius R = Diameter/2 = 0.2/2 =0.1 m

Initial Moment of inertia, MOI of cylinder + MOI of rod

so Inet = 1/2)*M*R2 +2*[(1/12)*m*L2+m*(R+L/2)^2]

I1=(1/2)*40*0.12+2* (1/12)*2.5*0.66^2 +2.5*(0.1+0.66/2)^2]

I1=1.306 Kg m^2

now Final Moment of inertia,

I2=(1/2)*M*R^2

I2=(1/2)*45*0.1^2 =0.225 Kg-m^2

By conservation of angular momentum , L1 = L2

i,e I1 W1 = I2 W2

1.306*0.8 = = 0.225*W2

W2=4.64 rev/s

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

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

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