Explanation Given: Constant torque T exerted on the flywheel. Retarding torque proportional to ω . Moment of inertia of the flywheel I and its initial angular velocity ω 0 . Approach: Use Newton’s second law for rotational motion, that is, moment of inertia × angular acceleration = sum of torques. Calculation: Retarding torque is, T r = − k ω . Newton’s second law for rotational motion gives: I d ω d t = τ + T = − k ω + T d ω T − k ω = d t I Let, ω = z 2 d ω = 2 z d z Substitute to get: 2 z d z T − k z = d t I z d z T / k − z = k 2 d t I ( z − T / k + T / k ) d z T / k − z = k 2 d t I − d z + ( T / k ) d z T / k − z = k 2 d t I Integrate to get:

Fundamentals Of Differential Equations And Boundary Value Problems, Books A La Carte Edition (7th Edition)

7th Edition

ISBN: 9780321977182

Author: Nagle, R. Kent, Saff, Edward B., Snider, Arthur David

Publisher: PEARSON

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3.4, Problem 16E

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Equation for the angular velocity ω as a function of time.

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Chapter 3.4, Problem 15E

Chapter 3.4, Problem 17E

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Fundamentals Of Differential Equations And Boundary Value Problems, Books A La Carte Edition (7th Edition)

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Equation for the angular velocity ω as a function of time.

Solution Summary: The author explains Newton's second law for rotational motion, that is, moment of inertia of the flywheel I and its initial angular velocity.

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To find: Equation for the angular velocity ω as a function of time.

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To find:

Equation for the angular velocity ω as a function of time.