Moment of inertia and angular speed of skater

AI Thread Summary
A 60kg skater starts spinning at an angular speed of 6 rad/s and reduces her moment of inertia by 50% by changing her arm position. The conservation of angular momentum principle indicates that the final angular speed can be calculated using the initial and final moments of inertia. The correct calculation shows that the final angular speed is 12 rad/s, not 9 rad/s as initially suggested. The discussion emphasizes the relationship between moment of inertia and angular speed in rotational motion. Understanding these concepts is crucial for solving problems related to angular momentum.
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Homework Statement


A 60kg skater begins a spin with an angular speed of 6 rad/s. By changing the position of her arms, the skater decreases her moment of intertia by 50%. What is the skater's final angular speed?


Homework Equations


I understand that I=m*(r^2), so if the radius decreases when she puts her arns in, then the initertia decreases.


The Attempt at a Solution



My attempt at this is that since it decreases by 50%, then the angular speed must increase by two to compensate. Is this correct and that her final speed is 9 rad/s?
 
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I=m*r^2 describes how to decrease moment of inertia - but doesn't tell you much about angular speed. You'll want to be thinking about angular momentum, which is conserved.
 
"My attempt at this is that since it decreases by 50%, then the angular speed must increase by two to compensate"

you are correct but 6 x 2 does not equal 9
 
Ah...

Lf = Lo
[I(final) * w(final)] = [I(initial) * w(initial)]
w(final) = [I(initial) * w(initial)] / I(final)

*If I(initial) = 2, and, I(initial) * 50%= 1, then her final speed is 12 rad/s.
 
Why I typed 9 I don't know... :D, I meant 12...
 
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