Concept explainers
Knowing that at the instant shown bar AB has angular velocity of 4 rad/s and an angular acceleration of 2 rad/s2, both clockwise, determine the angular acceleration (a) of bar BD, (b) of bar DE by using the
(a)
The angular acceleration of bar
Answer to Problem 15.133P
The angular acceleration of bar
Explanation of Solution
Given information:
The angular velocity of bar
Write the expression of position vector of a point.
YY1
Here, the coordinate in 3
The coordinate of point
The coordinate of point
The coordinate of point
Write the expression of angular velocity of
Here, the angular velocity of
Write the expression of angular acceleration of
Here, the angular acceleration of
Write the expression of velocity of point
Here, the angular velocity of
Write the expression of velocity of point
Here, the angular velocity of
Write the expression of velocity of point
Here, the angular velocity of
Write the expression of acceleration of point
Here, acceleration of point
Write the expression of acceleration of point
Here, the acceleration of point
Write the expression of acceleration of point
Here, the angular acceleration of link
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Here, the Equation (X) is the cross product of two vector, now change it in determinant form.
Substitute
Here, the Equation (XI) is the cross product of two vector, now change it in determinant form.
Substitute
Here, the Equation (XII) is the cross product of two vector, now change it in determinant form.
Compare the term of
Compare the term of
Substitute
Here, the Equation (XIV) is the cross product of two vector, now change it in determinant form.
Substitute
Here, the Equation (XV) is the cross product of two vector, now change it in determinant form.
Substitute
Here, the Equation (XVI) is the cross product of two vector, now change it in determinant form
Compare the term of
Compare the term of
Conclusion:
The angular acceleration of bar
(b)
The angular acceleration of bar
Answer to Problem 15.133P
The angular acceleration of bar
Explanation of Solution
Calculation:
Compare the term of
Conclusion:
The angular acceleration of bar
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Chapter 15 Solutions
Vector Mechanics for Engineers: Dynamics
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