Concept explainers
(a)
The maximum value of the angle
Answer to Problem 18.140P
The maximum value of the angle
Explanation of Solution
Given information:
The height of the solid cone is
Write the expression for the height of the center of gravity from the apex.
Here, the height of the solid cone is
Write the expression for the mass moment of the inertia.
Here, the mass of the solid cone is
Write the expression for the mass moment of the inertia in the transverse axis.
Write the expression for the angular velocity in the x- direction.
Here, the rate of the precession is
Write the expression for the angular velocity in y- direction.
Here, the rate of the change of the angle is
Write the expression for the angular velocity in z- direction.
Here, the rate of the spin is
Write the expression for the kinetic energy.
Write the expression for the potential energy.
Write the expression for the total energy.
Write the expression for the constant
Write the expression for the constant
Write the expression for the force.
Here, the distance along the x -axis is
Write the expression for the maximum angle.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Select the minimum value of
Substitute
Conclusion:
The maximum value of the angle
(b)
The corresponding value of the rate of precession.
The corresponding value of the rate of spin.
Answer to Problem 18.140P
The corresponding value of the rate of precession is
The corresponding value of the rate of spin is
Explanation of Solution
Write the expression for the rate of the precession.
Write the expression for the rate of the spin.
Calculation:
Substitute
Substitute
Conclusion:
The corresponding value of the rate of precession is
The corresponding value of the rate of spin is
(c)
The value of the angle at which the sense of precession is reversed.
Answer to Problem 18.140P
The value of the angle at which the sense of precession is reversed is
Explanation of Solution
Write the expression for the rate of the precession.
Calculation:
Substitute
Conclusion:
The value of the angle at which the sense of precession is reversed is
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Chapter 18 Solutions
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