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### 803-E: Ice Skater Spin Qualitative

• Topic Cluster: Rotational Motion
• Topic: Rotation Conservation Laws
• Objective: Using the formulas related to angular momentum, describe how an ice skater (or other athlete) changes her rotational speed.
• Content:
• Level: 2

#### BACK to Ladder Rotation Conservation Laws

In previous pods, we introduced the concept of angular momentum. Angular momentum is always conserved when their are no torques acting on some object. This principle can be used by athletes to control how quickly their body rotates. This quiz focuses on the most famous example of this technique: spinning figure skaters.

$$L = I \omega$$

The conservation of angular momentum states that, when no external torques are acting on some object, the angular momentum $$L$$ of that object remains constant.

The rotational inertia of a point mass is given by the formula $$I = m r^2$$. To find the rotational inertia of a person's arm, more complicated math is required. Nevertheless, the point mass formula contains the concept you need to understand: when mass is farther away form the axis of rotation, it contributes MORE to the rotational inertia than when it is close to the axis of rotation.

1. If no external torques act on an object, what is the proportionality relationship between rotational inertia and angular momentum?
• direct proportionality
• inverse proportionality
2. When a figure skater moves her arms inward, what happens to her rotational inertia? Explain why by referring explicitly to the formula for rotational inertia.
3. When a figure skater moves are arms outward, what happens to her rotational inertia? Explain why by referring explicitly to the formula for rotational inertia.
4. If there are no external torques, and rotational inertia increases (arms raised outward), what happens to angular velocity? Why?
5. If there are no external torques, and rotational inertia decreases (arms held inward), what happens to angular velocity? Why?
6. By putting together all of the analysis above, when a spinning figure skater pulls her arms inward, what should we observe?
7. By putting together all of the analysis above, when a spinning figure skater pulls her arms outward, what should we observe?
Wikipedia article on Biellmann spin.

The following two articles show a spinning figure skaters. At some points, a figure skater moves her arms inward in order to spin faster, than moves them outward when they want to stop spinning.