Concept explainers
(a)
The rate of precession
(a)
Answer to Problem 18.142P
The rate of precession
Explanation of Solution
Given information:
The position of the sphere
The largest value of
Calculation:
Conservation of angular momentum about the Z and z axes:
The only external forces are acting in homogenous sphere is weight of the sphere and reaction at A. Hence, the angular momentum is conserved about the Z and z axes.
Choose the principal axes
Write the expression for the angular velocity
The principal moment of inertia are
Draw the Free body diagram of homogeneous sphere and the forces acting on it as in Figure (1).
Write the expression for the angular momentum about point A.
Substitute
Consider
The scalar value of
Determine the conservation of angular momentum about fixed Z axis
Substitute
Substitute
Substitute
Determine the constant value using the angular momentum along z–axis.
Substitute
Substitute
Substitute 0 for constant in Equation (3).
Substitute 0 for
Conservation of energy:
Determine the value of kinetic energy T.
Substitute
Select the datum at
Determine the value of conservation of energy using the relation.
Here, E is the constant and V is the potential energy.
Substitute
Substitute
Substitute
Consider
Substitute
Substitute
Therefore, the rate of precession
(b)
The rates of precession
(b)
Answer to Problem 18.142P
The rate of precession
The rate of spin
Explanation of Solution
Given information:
The position of the sphere
The largest value of
Calculation:
Determine the rate of precession
Substitute
Therefore, the rate of precession
Determine the rate of spin
Substitute
The rate of spin
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Chapter 18 Solutions
Connect 2 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics
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