Conservation of Angular Momentum of ballerina

In summary, a ballerina is performing a tour jete with an initial angular speed and rotational inertia consisting of two parts. At her maximum height, she changes the angle of her legs and maintains her angular speed. The question asks for the ratio of her final and initial angular speeds. Using the equation L(final) = L(initial) and the fact that the change in theta is -60 degrees, the ratio can be found.
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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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  • #2
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.
 

FAQ: Conservation of Angular Momentum of ballerina

What is conservation of angular momentum?

Conservation of angular momentum is a fundamental principle in physics that states that the total angular momentum of a system remains constant as long as there are no external torques acting on it.

How does it apply to a ballerina spinning on one leg?

In the case of a ballerina spinning on one leg, the initial angular momentum of the system is conserved as she pulls her arms and legs closer to her body, resulting in an increase in her angular velocity.

What factors affect the conservation of angular momentum in this scenario?

The conservation of angular momentum in this scenario is affected by the moment of inertia of the ballerina, the distance of her limbs from her axis of rotation, and any external forces or torques acting on her, such as friction from the ground or air resistance.

Why does the ballerina's spin slow down when she extends her arms or legs?

When the ballerina extends her arms or legs, she increases her moment of inertia, which results in a decrease in her angular velocity in order to maintain the conservation of angular momentum.

How does the conservation of angular momentum relate to other laws of physics?

The conservation of angular momentum is related to other fundamental principles in physics, such as the conservation of energy and Newton's laws of motion. It can also be used to explain phenomena such as planetary orbits and the stability of spinning objects.

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