A 60.0-kg skater begins a spin with an angular speed of 6.0 rad/s. By changing the position of her arms, the skater decreases her moment of inertia by two times. What is the skater's final angular speed

The skater's final angular speed is equal to 12 rad/s.

Given the following data:

To determine the skater's final angular speed, we would use the law of conservation of angular momentum:

By applying the law of conservation of angular momentum, we have:

  ...equation 1.

Making the subject of formula, we have:

  ...equation 2

Note: The skater decreases her moment of inertia by two times.

Final moment of inertia, =  ...equation 3.

Substituting eqn. 3 into eqn. 2, we have:

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The final angular speed of the skater is 12 radians per second.

Explanation:

Let consider the skater as a rotating system, given the absence of external forces, the Principle of Angular Momentum Conservation is applied:

Where:

, - Initial and final moment of inertia, measured in .

, - Angular speed, measured in radians per second.

The final angular speed is cleared afterwards:

Given that and , the final angular speed is:

The final angular speed of the skater is 12 radians per second.

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