Concept explainers
(a)
Angular acceleration of bar BD.
Answer to Problem 15.132P
The angular acceleration of bar BD is
Explanation of Solution
Given information:
Angular velocity of bar AB is
Angular acceleration of bar AB is
The absolute value of point A
The relative velocity of A with respect to B is defined as
The absolute acceleration of point B is defined as:
The tangential acceleration is defined as:
The normal acceleration is defined as:
In above equations:
Calculation:
Position vector of B relative to A:
Position vector of D relative to B:
Position vector of D relative to E:
For bar AB:
Velocity of point B:
For bar BD:
Velocity of point D:
For bar DE:
Velocity of point D:
Equate above equations
Equate components:
Therefore:
For bar AB:
Acceleration of point B
We know that:
Therefore:
For bar BD:
Acceleration of point D:
Substitute:
Therefore:
For bar DE
Acceleration of point D:
Substitute:
Therefore:
Equate above equations
Equate components:
Solve above equations:
Conclusion:
The angular acceleration of bar BD is
(b)
Angular acceleration of bar DE
Answer to Problem 15.132P
The angular acceleration of bar DE is
Explanation of Solution
Given information:
Angular velocity of bar AB is
Angular acceleration of bar AB is
The absolute value of point A
The relative velocity of A with respect to B is defined as
The absolute acceleration of point B is defined as
The tangential acceleration is defined as
The normal acceleration is defined as
In above equations
Calculation:
According to sub part a
Acceleration of point D for bar BD
Acceleration of point D for bar DE
Equate above equations
Equate components
Therefore
Conclusion:
The angular acceleration of bar DE is
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Chapter 15 Solutions
Vector Mechanics For Engineers
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