Answered: A spinning disk with a mass of 12 kg…

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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Question

A spinning disk with a mass of 12 kg and a radius of 2 m has an angular velocity of 3 rad/s. What is the kinetic energy of the disk?

A. 24 J
B. 108 J
C. 162 J
D. 262 J

Expert Solution

Step 1

$Solution : Rotational kinetic energy of a disc K . \in = \frac{1}{2} I ω^{2} Where I = inertia = \frac{1}{2} {MR}^{2} R = radius = 2 m M = mass = 12 kg ω = angular speed = 3 rad / s K . \in = \frac{1}{2} (\frac{1}{2} {MR}^{2}) ω^{2} = \frac{{MR}^{2} ω^{2}}{4} = \frac{12 kg {(2 m)}^{2} \times {(3 rad / s)}^{2}}{4} K . \in = 108 J$

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