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Unless otherwise stated, in the following | Ch 3.4 - 17E

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 17E Chapter 3.4

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 17E

Problem

Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.

In Problem 16, let I = 50 kg-m2 and the retarding torque be  N-m. If 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.

Step-by-Step Solution:
Step 1 of 3

Step-1:

In this problem we need to find the time when the flywheel to come to rest.

Let us consider, the angular velocity is .

Torque from the motor is T.

The moment of inertia of flywheel is .

Initial angular velocity of the flywheel is .

Retarding torque due to friction is proportional to the angular velocity .

That is, , where k is the proportional constant.

By newton’s second law for rotation of motion we have:.

That is,

                       

Therefore,

Step-2:

Given:

Proportionality constant k = 5.

Angular velocity  and

We know that , at the initial stage motor is turned off.So,T=0.

Now the above equation becomes:

.

Now it is in variable separable form.

Integrating on both sides we get.

Step 2 of 3

Chapter 3.4, Problem 17E is Solved
Step 3 of 3

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

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Unless otherwise stated, in the following | Ch 3.4 - 17E

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