Concept explainers
(a)
The angular acceleration of the plate.
Answer to Problem 16.162RP
The angular acceleration of the plate is
Explanation of Solution
Given information:
The side of the square plate is
The following figure represents the general plane flow.
Figure-(1)
Write the expression for the distance between the point A and G.
Here, the distance between the point A and G is
Write the expression for the angular acceleration.
Here, the vector position between the point A and G is
Substitute
Write the expression for the acceleration at point A.
Here, the acceleration at point A is
Write the expression for the acceleration at point B.
Here, the acceleration at point B is
Write the expression for the direction of the acceleration.
Here, the direction of the acceleration is
Substitute
The following figure represents the acceleration diagram.
Figure-(2)
Write the expression for the angle.
He3re, the angle is
Write the expression for the distance between the point A and the point E.
Here, distance between the point A and the point E is
Write the expression for the distance between the point E and the point G along
Here, the distance between the point E and the point G in
Write the expression for the distance between the point E and the point G.
Here, the distance between the point E and the point G in
Write the expression for the resultant EG.
Here, the resultant EG is
Substitute
The following figure represents the free body diagram of the applied forces.
Figure-(3)
Write the expression for the acceleration at point G.
Here, the acceleration at point G is
Write the expression for the forces along
Here, the acceleration along
Write the expression for the forces along
Here, the acceleration along
Write the expression for the moment of inertia.
Here, the radius of gyration is
Write the expression for the radius of gyration.
Substitute
Write the expression for the moments about B.
Substitute
Substitute
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The angular acceleration of the plate is
(b)
The reaction at the corner A.
Answer to Problem 16.162RP
The reaction at the corner A is
Explanation of Solution
Given information:
The side of the square plate is
The following figure represents the general plane flow.
Figure-(4)
Write the expression for the reaction at corner A.
Here, the reaction force at point A is
Substitute
Substitute
Calculation:
Substitute
Conclusion:
The reaction at the corner A is
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Chapter 16 Solutions
Vector Mechanics for Engineers: Dynamics
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