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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman
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A gyroscope is precessing about a vertical axis. Describe

Chapter 4, Problem 55E

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QUESTION:

A gyroscope is precessing about a vertical axis. Describe what happens to the precession angular speed if the following changes in the variables are made, with all other variables remaining the same: (a) the angular speed of the spinning flywheel is doubled; (b) the total weight is doubled; (c) the moment of inertia about the axis of the spinning flywheel is doubled; (d) the distance from the pivot to the center of gravity is doubled. (e) What happens if all four of the variables in parts (a) through (d) are doubled?

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QUESTION:

A gyroscope is precessing about a vertical axis. Describe what happens to the precession angular speed if the following changes in the variables are made, with all other variables remaining the same: (a) the angular speed of the spinning flywheel is doubled; (b) the total weight is doubled; (c) the moment of inertia about the axis of the spinning flywheel is doubled; (d) the distance from the pivot to the center of gravity is doubled. (e) What happens if all four of the variables in parts (a) through (d) are doubled?

ANSWER:

Solution 55E Introduction We have to discuss how the precession changes if the given parameter changes. Step 1 The angular velocity of precession is given by Here I is the moment of inertia of the gyroscope about its axis, and is the angular speed of spin, r is the distance or center of mass from the pivot and w is the weight. (a) From the above equation we can see that the precession speed inversely proportional to the angular speed of spin. Hence if th

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