Concept explainers
(a)
The condition for steady precision.
Answer to Problem 18.110P
The condition for steady precision is
Explanation of Solution
Given information:
The below figure represent the schematic diagram of the system.
Figure-(1)
Write the expression angular velocity.
Here, the precision rate is
Write the expression of angular momentum about the centroid
Here, the moment of inertia about the
Write the expression of angular momentum about the centroid
Here, the inertia about the reference frame is
Write the expression of angular velocity about the reference frame.
Write the expression of the total moment.
Substitute
Write the expression of moment about
Here, the weight is
Substitute
Conclusion:
The condition for steady precision is
(b)
The condition of steady precision if the rate of spin of the top is very large compared with its rate of precision.
Answer to Problem 18.110P
The condition of steady precision if the rate of spin of the top is very large compared with its rate of precision is
Explanation of Solution
Write the expression of
Substitute
Here, the term
Conclusion:
The condition of steady precision if the rate of spin of the top is very large compared with its rate of precision is
(c)
The percentage error.
Answer to Problem 18.110P
The percentage error is
Explanation of Solution
Given information:
Mass of the top is
Write the expression of weight.
Here, the acceleration due to gravity is
Write the expression of pin rate.
Here, the number of revolution is
Write the expression of inertia about the transverse axis.
Here, the radius of gyration is
Write the expression of inertia.
Here, the radius of gyration is
Write the expression of percentage error.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The percentage error is
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Chapter 18 Solutions
Vector Mechanics For Engineers
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