Explanation Since there is no external torque acting between spacecraft and gyroscope, the angular momentum of both spacecraft and gyroscope is conserved. The direction of turning of spacecraft and gyroscope are opposite to each other. Let I 1 be the moment of inertia of the gyroscope, I 2 be the moment of inertia of spacecraft. Write the expression for conservation of momentum of both spacecraft and gyroscope. p i = p f (I) Here, p i is the initial momentum, and p f is the final momentum. The initial momentum of spacecraft and gyroscope is zero, and the final momentum is the sum of the momentum of spacecraft and gyroscope. Substitute, 0 for p i , and I 1 ω 1 + I 2 ω 2 for p f in equation (I). 0 = I 1 ω 1 + I 2 ω 2 I 1 ω 1 = − I 2 ω 2 (II) Here, ω 1 is the angular velocity of the gyroscope, and ω 2 is the angular velocity of spacecraft. Substitute, θ t for ω 2 in equation (II), and rearrange to obtain an expression for t . I 1 ω 1 = − I 2 ( θ t ) t = − I 2 ( θ I 1 ω 1 ) (III) Here, θ is the angular displacement, and t is the time

Principles of Physics: A Calculus-Based Text

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ISBN: 9781133104261

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Definition Definition Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.

Chapter 10, Problem 63P

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The operation time of the gyroscope.

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Chapter 10, Problem 62P

Chapter 10, Problem 64P

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The operation time of the gyroscope.

Solution Summary: The author explains the angular momentum of both spacecraft and gyroscope, and the direction of turning.

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