Concept explainers
(a)
The velocity of the mass centre
Answer to Problem 18.28P
The velocity of the mass centre
Explanation of Solution
Given information:
The mass of the each plate is
Write the expression for moment of the inertia about the x- axis.
Here, the distance of mass centre from the circular plate is
Write the expression for moment of the inertia about the y- axis.
Write the expression for moment of the inertia about the z- axis.
Write expression for the product moment of inertia about the plane
Write expression for the product moment of inertia about the plane
Write expression for the product moment of inertia about the plane
The figure below shows the effective kinetic diagram of the system.
Figure-(1)
Write the expression for the impulse about point
Write the expression for the velocity of the mass centre of the system.
Here, the velocity of the mass centre in x- direction is
Calculation:
For upper plate:
Substitute
Substitute
Substitute
Substitute
For lower plate:
Substitute
Substitute
Substitute
Substitute
For assembly the inertia of the moment of both the plate is added.
Substitute
Compare coefficient of
Compare coefficient of
Compare coefficient of
Substitute
Conclusion:
The velocity of the mass centre
(b)
The angular velocity of the assembly.
Answer to Problem 18.28P
The angular velocity of the assembly is
Explanation of Solution
Write the expression for the moments about centre point
Here, the angular momentum about x- direction is
Write the expression for the angular momentum in x- direction.
Write the expression for the angular momentum in y- direction.
Write the expression for the angular momentum in z- direction.
Write the expression for the angular velocity of the assembly.
Calculation:
Substitute
Compare coefficient of
Compare coefficient of
Compare coefficient of
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The angular velocity of the assembly is
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Chapter 18 Solutions
Vector Mechanics For Engineers
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