Answered: How much rotational kinetic energy in…

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

How much rotational kinetic energy in joules is there in a disk of radius 0.2 meters and mass 33 kg rotating at 1000 turns per second? Give your answer in joules.

Expert Solution

Step 1

The equation for the rotational kinetic energy is,

$K . E . = \frac{1}{2} I ω^{2}$

Here, $I$ is the moment of inertia,

$ω$ is the angular speed.

For a disk, moment of inertia is,

$I = \frac{1}{2} m R^{2}$

Here, m is the mass and R is the radius.

Thus, the above equation of kinetic energy becomes,

$K . E . = \frac{1}{2} (\frac{1}{2} m R^{2}) ω^{2} = \frac{1}{4} m R^{2} ω^{2}$

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