### Understanding Moments of Inertia and Angular Velocity#### Problem Statement:A figure skater wants to spin faster. With her arms and legs outstretched, she has a moment of inertia $ I $ = 3.6 kgm$^2$ and a spin rate of 2.0 rev/s. If she can squeeze her arms and legs closer to her rotation axis, she can spin at a rate of 24 rev/s. What is her new moment of inertia for the faster spin?#### Options:- 1.9 kgm$^2$- 0.30 kgm$^2$- 7.2 kgm$^2$- 45 kgm$^2$#### Explanation:The relationship between the moment of inertia $ I $ and angular velocity $ \omega $ for a rotating body is governed by the conservation of angular momentum. Angular momentum $ L $ is given by:\[ L = I \omega \]Since angular momentum is conserved, the initial angular momentum $ L_1 $ must equal the final angular momentum $ L_2 $:\[ L_1 = L_2 \]Therefore:\[ I_1 \omega_1 = I_2 \omega_2 \]Given:- $ I_1 = 3.6 $ kgm$^2$- $ \omega_1 = 2.0 $ rev/s- $ \omega_2 = 24 $ rev/sWe need to find $ I_2 $:\[ I_2 = \frac{I_1 \omega_1}{\omega_2} \]Substitute the values:\[ I_2 = \frac{3.6 \, \text{kgm}^2 \times 2.0 \, \text{rev/s}}{24 \, \text{rev/s}} \]\[ I_2 = \frac{7.2 \, \text{kgm}^2 \text{ rev/s}}{24 \, \text{rev/s}} \]\[ I_2 = 0.30 \, \text{kgm}^2 \]Hence, the correct answer is:\[ \boxed{0.30 \, \text{kgm}^2} \]

Answered: Image /qna-images/answer/dac9e494-15b2-4c49-85c7-84ba28e54d6f.jpg

A figure skater wants to spin faster. With her arms and leg outstretched, she has a moment of inertia1 = 3.6 kgm2 and a spin rate of 2.0 rev/s. If she can squeeze her arms and leg closer to her rotation axis, she can spin at a rate of 24 rev/s. What is her new moment of inertia for the faster spin? O 1.9 kgm2 O 0.30 kgm2 O 7.2 kgm2 O 45 kgm2

A figure skater wants to spin faster. With her arms and leg outstretched, she has a moment of inertia1 = 3.6 kgm2 and a spin rate of 2.0 rev/s. If she can squeeze her arms and leg closer to her rotation axis, she can spin at a rate of 24 rev/s. What is her new moment of inertia for the faster spin? O 1.9 kgm2 O 0.30 kgm2 O 7.2 kgm2 O 45 kgm2

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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