Concept explainers
The largest value of
Answer to Problem 18.141P
The largest value of
Explanation of Solution
Given information:
The position of the sphere
The rate of precession
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
Solve the Equation (7).
The value of
Determine the largest value of
Therefore, the largest value of
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Chapter 18 Solutions
Vector Mechanics for Engineers: Statics and Dynamics - With Access
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