Concept explainers
(a)
The couple
(a)
Answer to Problem 18.102P
The couple
Explanation of Solution
Given information:
The weight (W) of the disk is 6 lb.
The radius (r) of the disk is 3 in..
The angular velocity
The angular velocity of shaft CBD and arm AB
The horizontal distance (c) between the center of rod CBD and center of disk is 5 in..
The vertical distance (b) between the center of rod CBD and center of disk is 4 in..
The couple
The time (t) of couple applied is 3 s.
Calculation:
Find the mass (m) of the disk using the equation:
Here, g is the acceleration due to gravity.
Substitute 6 lb for W and
Write the equation of vector form of angular velocity
The angular velocity
Write the equation of angular velocity of disk A
Write the equation of angular velocity
Find the equation of angular velocity
Substitute 0 for
Find the equation of angular momentum about A
Substitute 0 for
Find the rate of change of angular momentum
Here,
Write the equation of the rate of change of angular momentum about A
Substitute
Write the equation mass moment of inertia
Write the equation mass moment of inertia
Write the equation of velocity of the mass center A of the disk.
Write the equation of acceleration of the mass center A of the disk.
Substitute
Find the position vector of D with respect to A.
Substitute 5 in. for c and 4 in. for b.
Find the rate of change of angular momentum about D
Substitute
Substitute
Sketch the free body diagram and kinetic diagram of the system as shown in Figure (1).
Refer Figure (1),
Apply Newton’s law of motion.
Substitute
Equate i-vector coefficients in Equation (3).
Equate k-vector coefficients in Equation (3).
Take moment about D.
Here,
The moment at D is equal to the rate of change of angular momentum at D.
Equate Equation (3) and (7).
Find the angular acceleration
Substitute 0 for
Find the couple
Substitute 3 in. for r, 5 in. for c,
Thus, the couple
(b)
The dynamic reaction at C and D after the couple has been removed.
(b)
Answer to Problem 18.102P
The dynamic reaction at C after the couple has been removed is
The dynamic reaction at D after the couple has been removed is
Explanation of Solution
Calculation:
After the 3 s, the couple
Find the component of dynamic reaction at C
Substitute 4 in. for b, 3 in. for r, 5 in. for c, 18 rad/s for
Find the component of dynamic reaction at D
Substitute 4 in. for b, 3 in. for r, 5 in. for c, 18 rad/s for
Find the component of dynamic reaction at C
Substitute 4 in. for b, 3 in. for r, 60 rad/s for
Find the component of dynamic reaction at D
Substitute 4 in. for b, 3 in. for r, 60 rad/s for
Find the dynamic reactions at C using the equation:
Substitute
Thus, the dynamic reactions at C after the couple has been removed is
Find the dynamic reactions at D using the equation:
Substitute
Thus, the dynamic reactions at D after the couple has been removed is
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Chapter 18 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
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