2. A figure skater is spinning at a rate of 10.0 rad/s with her arms horizontall
ID: 1793210 • Letter: 2
Question
2. A figure skater is spinning at a rate of 10.0 rad/s with her arms horizontally extended and her moment of inertia of 2.50 kg.m a) b) c) When she pulls her arms in close to her body, will her angular speed increase, decrease or remain the same? Explain the correct answer using correct physics principles What is her angular speed after she pulls her arms in and reduces her moment of inertia to 1.60 kg m2? (15.6 rad/s) Calculate her kinetic energy before and after she pulls her arms in. Is kinetic energy conserved? If kinetic was lost, where did it go? If kinetic energy was gained, where did it come from?Explanation / Answer
2)Given,
w1 = 10 rad/s ; I1 = 2.5 kg-m^2
a)From conservation of angular momentum, the angular speed will increase since the moment of inertia will decrease.
b)I2 = 1.6 kg-m^2
from conservation of angular momentum
Li = Lf
I1w1 = I2w2
w2 = I1w1/I2 = 2.5 x 10/1.6 = 15.6 rad/s
Hence, w2 = 15.6 rad.
c)KEi = 1/2 I1 w1^2
KEi = 0.5 x 2.5 x 10^2 = 125 J
KEf = 1/2 I2 w2^2
KEf = 0.5 x 1.6 x 15.6^2 = 194.6 J
Hence, KEi = 125 J ; KEf = 194.6 J
The kinetic energy is not conserved.
It has increased since the rotational speed has been increased, because of the decrease in angular momentum of the skater, in accordance with the law of conservation of angukar momentum.
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