### Understanding Angular AccelerationWhen a fan is turned off, its angular speed reduces over time. In this exercise, we examine how the angular speed of a fan decreases and calculate the angular acceleration. Angular acceleration can be defined as the rate of change of angular velocity and is measured in radians per second squared (rad/s²).#### Problem Statement:A fan is turned off, and its angular speed decreases from 10.0 rad/s to 6.3 rad/s in 5.0 seconds. What is the magnitude of the angular acceleration of the fan?#### Given:- Initial angular speed, \( \omega_0 = 10.0 \) rad/s- Final angular speed, \( \omega = 6.3 \) rad/s- Time interval, \( t = 5.0 \) seconds#### Formula:The angular acceleration \( \alpha \) is calculated using the formula:\[ \alpha = \frac{\Delta \omega}{\Delta t} \]where \( \Delta \omega \) is the change in angular speed and \( \Delta t \) is the time interval.#### Calculation:\[ \alpha = \frac{6.3 \, \text{rad/s} - 10.0 \, \text{rad/s}}{5.0 \, \text{s}} \]\[ \alpha = \frac{-3.7 \, \text{rad/s}}{5.0 \, \text{s}} \]\[ \alpha = -0.74 \, \text{rad/s}^2 \]Since we are asked for the magnitude of the angular acceleration, we take the absolute value:\[ |\alpha| = 0.74 \, \text{rad/s}^2 \]#### Answer Choices:- ○ 0.86 rad/s²- ○ 0.74 rad/s²- ○ 0.37 rad/s²- ○ 11.6 rad/s²- ○ 1.16 rad/s²The correct answer is:- ○ **0.74 rad/s²**### ConclusionBy using the change in angular speeds and the time interval, we determined the magnitude of the angular acceleration of the fan is 0.74 rad/s². This process demonstrates the method of calculating angular acceleration when the initial and final angular speeds, along with the time interval, are known.

Answered: Image /qna-images/answer/fd615e5b-5c5a-4ef2-b5a9-dd10ffe6547f.jpg

A fan is turned off, and its angular speed decreases from 10.0 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the angular acceleration of the fan? 0.86 rad/s2 0.74 rad/s2 0.37 rad/s2 O 11.6 rad/s2 1.16 rad/s2

A fan is turned off, and its angular speed decreases from 10.0 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the angular acceleration of the fan? 0.86 rad/s2 0.74 rad/s2 0.37 rad/s2 O 11.6 rad/s2 1.16 rad/s2

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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