Concept explainers
Knowing that at the instant shown bar AB has a constant angular velocity of 4 rad/s clockwise, determine the angular acceleration (a) of bar BD, (b) of bar DE.
(a)
The angular acceleration of the bar BD.
Answer to Problem 15.131P
The angular acceleration of the link BD is
Explanation of Solution
Given information:
The angular velocity of the bar is
The following figure represents the different types of the bar.
Figure-(1)
The unit vector along the
Write the expression for the velocity at point B.
Here, the velocity at point B is
Write the expression for the velocity at point D link BD.
Here, the velocity at point D with link BD is
Write the expression for the velocity at point D with link DE.
Here, the angular velocity of the link DE is
Write the expression for the acceleration of the point B.
Here, the acceleration of the point B is
Write the expression for the acceleration of the point D with a part of the link BD.
Here, the acceleration at point D with a part of the link BD is
Write the expression for the acceleration of the point D with a part of the link DE.
Here, the acceleration at point D with a part of the link DE is
Write the expression for the position of the unit vector for the link AB with respect to point D.
Here, the horizontal distance between the point B and the point E is
Write the expression for the position of the unit vector for the link DE with respect to point D.
Here, the vertical distance between the point D and the point E is and the unit vector for the link DE with respect to point D is
The angular acceleration of the link AB is zero because it has constant angular velocity.
Calculation:
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Conclusion:
The angular acceleration of the link BD is
(b)
The angular acceleration of the link DE.
Answer to Problem 15.131P
The angular acceleration of the link DE is
Explanation of Solution
Given information:
The angular velocity of the bar is
Calculation:
Compare
Conclusion:
The angular acceleration of the link DE is
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Chapter 15 Solutions
Vector Mechanics for Engineers: Dynamics
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