Concept explainers
15.133 and 15.134 Knowing that at the instant shown bar AB has an angular velocity of 10 rad/s and an angular acceleration of 4 rad/s2, both clockwise, determine the angular acceleration of (a) bar BD, (b) bar DE by using the
Fig. P15.131 and P15.133
(a)
Find the magnitude of angular acceleration of bar BD.
Answer to Problem 15.133P
The angular acceleration of the bar BD is
Explanation of Solution
Given information:
The angular velocity of the bar AB is
Consider the bar AB.
Consider the position of the point B with respect to the point A is denoted by
Calculate the velocity at B using the relation:
Substitute
Consider the bar BD.
Consider the position of the point D with respect to the point B is
Consider the angular acceleration of the bar BD is
Calculate the velocity of the point D using the relation:
Substitute
Consider the bar DE.
Consider the position of the point D with respect to the point E is
Consider the angular acceleration of the bar DE is
Calculate the velocity of the point D using the relation:
Substitute
Equate the Equation (1) and (2).
Equate j component of the Equation (3).
Equate i component of the Equation (3).
Substitute
Consider the bar AB.
The angular velocity of the bar AB is
The angular velocity of the bar BD is
The angular velocity of the bar DE is
The angular acceleration of the bar AB is
The angular acceleration of the bar BD is
The angular acceleration of the bar DE is
Consider the bar AB.
Calculate the acceleration
Substitute
Consider the bar BD.
Calculate the acceleration of the point D using the relation:
Substitute
Consider the bar DE.
Consider the angular acceleration of the bar DE is
Calculate the acceleration of the point D using the relation:
Substitute
Equate Equation (4) and (5)
Equate i component of the Equation (6).
Equate j component of the Equation (6).
Substitute
Thus, the angular acceleration of the bar BD is
(b)
Find the magnitude of angular acceleration of bar DE.
Answer to Problem 15.133P
The magnitude of the angular acceleration of bar DE is
Explanation of Solution
Given information:
Calculation:
Refer Part (a).
The angular acceleration of the bar DE is
Thus, The magnitude of the angular acceleration of bar DE is
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