Conservation of Angular Momentum of ballerina

AI Thread Summary
The discussion centers on a physics problem involving the conservation of angular momentum as a ballerina performs a tour jete. The initial and final angular speeds, along with the rotational inertia of her leg and trunk, are analyzed to find the ratio of final to initial angular speed. The user expresses confusion about the treatment of the legs in the calculations, specifically why only one leg's inertia is included initially while both legs are considered later. The conservation principle, L(final) = L(initial), is applied, leading to a solution that clarifies the problem. Ultimately, the user resolves their confusion and finds the problem less challenging than initially perceived.
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Homework Statement


I am new to Physics Forums and was wondering if anyone would be willing to help me with this problem.

A ballerina begins a tour jete with an angular speed ω(initial) and a rotational inertia consiting of two parts: I(leg) = 1.44 kg*m^2 for her leg extended outward at angle theta=90.0 degrees to her body and I(trunk)= 0.660 kg*m^2 for the rest of her body (primarily her truck). Near her maximum height she holds both legs at angle theta=30.0 degrees to her body and has angular speed ω(final). Assuming that I(trunk) has not changed, what is the ratio ω(final)/ω(initial).

Homework Equations



L(final) = L(initial)
L = Iω
The change in theta = -60 degrees.

The Attempt at a Solution



L(final leg) + L(final trunk) = L(initial leg) + L(initial trunk)
so,
(ω(final))(I(final leg) + 0.660 kg*m^2) = (ω(initial))(2.1 kg*m^2)

I have 3 unknowns and do not know what to do with the angles. Can anyone help me with the next thought?
 
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It took me a while, but I figured this one out. It actually wasn't as difficult as I thought. I still don't know why only one leg is considered in the initial equation while both legs are considered in the final equation.
 
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