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A skater goes into a spin with her arms pulled in (close to her body). When she stretches her arms out: A) her angular speed ω decreases due to her moment of inertia decreasing; B) her angular speed ω increases due to her moment of inertia decreasing; C) her angular speed ω decreases due to her moment of inertia decreasing; D) her angular speed ω increases due to her moment of inertia being constant;

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Anzanzio

Answer:

When she stretches her arms out, B) her angular speed ω increases due to her moment of inertia decreasing

Explanation:

The angular momentum of a rotating object is defined as the product of its moment of inertia and angular speed.

L = I ω

where

  • L is the angular momentum
  • I is the moment of inertia
  • ω is the angular speed

According to the principle of conservation of angular momentum, if there is no external torque, angular momentum of the skater must remain conserved. If the initial and final moment of inertia is I_i and I_f  while corresponding angular velocities are ω_i and ω_f , then the principle of conservation of angular momentum can be expressed as the following equation:

(I_f) (ω_f) = (I_i) (ω_i)

ω_f / ω_i = I_i / I_f

From the expression above, we can see that if the moment of inertia decreases, angular velocity would increase to conserve angular momentum of the skater.

Therefore, When she stretches her arms out, her angular speed ω increases due to her moment of inertia decreasing.

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