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 Integrate to get: − 1 k ln ( T − k ω ) = t I + C T − k ω = A exp ( − k t I ) ω = 1 k ( T − A exp ( − k t I ) ) Using the initial condition: ω ( 0 ) = ω 0 to get,

Fundamentals of Differential Equations [With CDROM] - 7th Edition

7th Edition

ISBN: 9780321410481

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

Publisher: Addison Wesley

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Chapter 3.4, Problem 15E

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

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Chapter 3.4, Problem 14E

Chapter 3.4, Problem 16E

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Fundamentals of Differential Equations [With CDROM] - 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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Chapter 3 Solutions

To find:

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