---
title: "A figure skater is spinning on frictionless ice with their arms outstretched, having an initial rotational inertia \\(I_0\\) and rotating with angular speed \\(\\omega_0\\). By pulling their arms inward toward their body, the skater reduces their rotational inertia to \\(\\dfrac{1}{3}I_0\\). What is the ratio of the skater’s final rotational kinetic energy to their initial rotational kinetic energy, \\(\\dfrac{K_f}{K_i}\\)?"
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url: "https://nerd-notes.com/ubq/120881/"
date_modified: "2026-08-23T04:44:09+00:00"
---

# A figure skater is spinning on frictionless ice with their arms outstretched, having an initial rotational inertia \(I_0\) and rotating with angular speed \(\omega_0\). By pulling their arms inward toward their body, the skater reduces their rotational inertia to \(\dfrac{1}{3}I_0\). What is the ratio of the skater’s final rotational kinetic energy to their initial rotational kinetic energy, \(\dfrac{K_f}{K_i}\)?

A figure skater is spinning on frictionless ice with their arms outstretched, having an initial rotational inertia \(I_0\) and rotating with angular speed \(\omega_0\). By pulling their arms inward toward their body, the skater reduces their rotational inertia to \(\dfrac{1}{3}I_0\). What is the ratio of the skater's final rotational kinetic energy to their initial rotational kinetic energy, \(\dfrac{K_f}{K_i}\)?

- **A.** \(\dfrac{1}{3}\)
- **B.** \(3\)
- **C.** \(9\)
- **D.** \(27\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120881/*