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aetteews
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A 47 kg figure skater is spinning on the toes of her skates at 1.5 rev/s. Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (42 kg, 20 cm average diameter, 160 cm tall) plus two rodlike arms (2.5 kg each, 62 cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20cmdiameter, 200cmtall cylinder.
 2 years ago
 2 years ago
aetteews Group Title
A 47 kg figure skater is spinning on the toes of her skates at 1.5 rev/s. Her arms are outstretched as far as they will go. In this orientation, the skater can be modeled as a cylindrical torso (42 kg, 20 cm average diameter, 160 cm tall) plus two rodlike arms (2.5 kg each, 62 cm long) attached to the outside of the torso. The skater then raises her arms straight above her head, where she appears to be a 45 kg, 20cmdiameter, 200cmtall cylinder.
 2 years ago
 2 years ago

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Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
Change in the angular momentum. What is the questions btw? What do I need to solve? lol
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
You want me to get the speed/angular velocity after she raises her hand?
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
Lol I just lost $150 :/
 2 years ago

saifoo.khan Group TitleBest ResponseYou've already chosen the best response.0
LOl. :/ @Ishaan94
 2 years ago

aetteews Group TitleBest ResponseYou've already chosen the best response.0
Why did you lose $150?
 2 years ago

aetteews Group TitleBest ResponseYou've already chosen the best response.0
No, umm... I need to find her rotation frequency in rev/s.
 2 years ago

eashmore Group TitleBest ResponseYou've already chosen the best response.2
We need to use the idea of conservation of angular momentum. This states, as applied to this particular example, that the skaters angular momentum will remain the same with her arms outstretched and with her arms above her head. Let's let subscript 1 indicate the case where her arms are outstretched and subscript 2 indicate the case where her arms are over head. We know that angular momentum is expressed as\[L = I \omega\]where \(I\) is the moment of inertia and \(\omega\) is the angular velocity in rad/s. Refer here for a list of moments of inertia: http://en.wikipedia.org/wiki/List_of_moments_of_inertia First, let's calculate the skaters moment of inertia in Case 1. Her moment of inertia can be represented as the sum of three separate, easy to represent geometric figures. 1) Her toros as a cylinder (8th row of the table at the above link.) 2 &3) Her arms as thin rods whose axis of rotation is at the end (3rd row) This sum is expressed as\[I_1 = I_{Cyl} + I_{arm} + I_{arm} = I_{cyl} + 2 I_{arm} = {m_tr^2 \over 2} + 2 \cdot \left [m_aL^2 \over 3 \right ] \] where \(m_t\) is the mass of the skater's torso, \(r\) is the radius of the skaters torso, \(m_a\) is the mass of the skater's arms, and \(L\) is the length of the skater's arms. The skater's moment of inertia in Case 2 can be modeled as a cylinder\[I_2 = {m_2 r^2 \over 2}\] where \(m_2 = 45 kg\) and \(r\) is the radius of the torso (same as in Case 1). Now, we can set up an expression for the conservation of angular momentum as\[I_1 \omega_1 = I_2 \omega_2\]
 2 years ago

VincentLyon.Fr Group TitleBest ResponseYou've already chosen the best response.0
This is a typical case of a nonsolid system, in which angular momentum is conserved, whereas kinetic energy is not
 2 years ago
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