Conservation of Angular Momentum of ballerina

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SUMMARY

The discussion focuses on the conservation of angular momentum in a ballerina's tour jete, specifically analyzing the relationship between her initial and final angular speeds (ω(initial) and ω(final)). The ballerina's rotational inertia is divided into two components: I(leg) = 1.44 kg*m² for her extended leg and I(trunk) = 0.660 kg*m² for her trunk. The conservation equation L(final) = L(initial) leads to the conclusion that the ratio ω(final)/ω(initial) can be derived from the equation (ω(final))(I(final leg) + 0.660 kg*m²) = (ω(initial))(2.1 kg*m²), where the change in angle is -60 degrees. The discussion highlights the importance of understanding how angular momentum is conserved despite changes in the configuration of the ballerina's body.

PREREQUISITES
  • Understanding of angular momentum and its conservation principles
  • Familiarity with rotational inertia calculations
  • Knowledge of basic trigonometry, particularly angle conversions
  • Ability to manipulate equations involving multiple variables
NEXT STEPS
  • Study the principles of rotational dynamics in classical mechanics
  • Learn about the moment of inertia for various shapes and configurations
  • Explore the effects of angular velocity changes on rotational systems
  • Investigate real-world applications of angular momentum conservation in dance and sports
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in the mechanics of motion, particularly in the context of dance and athletic performance.

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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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