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Answers without the blur. Sign up and see all textbooks for free! Q3-3.4-17E

Expert-verified Found in: Page 116 ### Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069 # In Problem 16, let I = 50 kg-m2 and the retarding torque be N-mIf the motor is turned off with the angular velocity at 225 rad/sec, determine how long it will take for the flywheel to come to rest.

The flywheel takes to come to rest in 300 sec.

See the step by step solution

## Step 1: Find the value of time

The equation is

$\mathrm{I}\frac{\mathrm{d}\omega }{\mathrm{dt}}=-{\mathrm{T}}_{1}\phantom{\rule{0ex}{0ex}}50\frac{\mathrm{d}\omega }{\mathrm{dt}}=-5\sqrt{\omega }\phantom{\rule{0ex}{0ex}}-10\int \frac{\mathrm{d}\omega }{\sqrt{\omega }}=\int \mathrm{dt}\\mathrm{begingathered}-20\sqrt{\mathrm{\omega }}=\mathrm{t}+\mathrm{c}\phantom{\rule{0ex}{0ex}}\mathrm{\omega }\left(\mathrm{t}\right)=\left(-\frac{\mathrm{t}}{20}+\mathrm{c}{\right)}^{2}\phantom{\rule{0ex}{0ex}}\\mathrm{endgathered}\phantom{\rule{0ex}{0ex}}-20\sqrt{\mathrm{\omega }}=\mathrm{t}+\mathrm{c}\phantom{\rule{0ex}{0ex}}\mathrm{\omega }\left(\mathrm{t}\right)=\left(-\frac{\mathrm{t}}{20}+\mathrm{c}{\right)}^{2}\phantom{\rule{0ex}{0ex}}$

## Step 2: Apply the given conditions

When ${\omega }_{0}$ = 225 , c = 15

$\omega \left(\mathrm{t}\right)=\left(-\frac{\mathrm{t}}{20}+15{\right)}^{2}\phantom{\rule{0ex}{0ex}}\mathrm{t}=20\left(15-\sqrt{\omega \left(\mathrm{t}\right)}\right)\phantom{\rule{0ex}{0ex}}$

at the moment when flywheel stopes rotating (t)=0,

so, t = 300 sec

Hence, the flywheel takes to come to rest in 300 sec. ### Want to see more solutions like these? 