Concept explainers
(a)
Angular acceleration of bar BD.
Answer to Problem 15.161P
The angular acceleration
Explanation of Solution
Given information:
Constant angular velocity of rod AE is
The constant relative velocity of pin P with respect to rod AE is
Plane motion of a particle relative to a rotating frame is defined as
In above equation
The Coriolis acceleration is a combination of:
Where
The Coriolis acceleration is defined as:
Calculation:
Length of AP
Length of BP
Velocity
Velocity
Velocity
Velocity
Velocity
Velocity
Equate components in equations 1 and 2.
Solve above equations:
Therefore:
Acceleration
The Coriolis acceleration
The acceleration
Acceleration
Acceleration
The Coriolis acceleration
The acceleration
Equate components in equations 1 and 2.
Solve above equations.
Conclusion:
The angular acceleration
(b)
The relative acceleration of pin P with respect to bar BD
Answer to Problem 15.161P
The relative acceleration
Explanation of Solution
Given information:
Constant angular velocity of rod AE is
The constant relative velocity of pin P with respect to rod AE is
Plane motion of a particle relative to a rotating frame is defined as
In above equation
The Coriolis acceleration is a combination of
Where
The Coriolis acceleration is defined as
Calculation:
According to sub part a
We have found
Acceleration
Solve above equations
Therefore
The magnitude and angle
Conclusion:
The relative acceleration
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics For Engineers
- A series of small machine components being moved by a conveyor belt pass over a 120 mm radius idler pulley. At the instant shown, the velocity of Point A is 300 mm/s to the left and its acceleration is 180 mm/s2 to the right. Determine (a) the angular velocity and angular acceleration of the idler pulley, (b) the total acceleration of the machine component at B.arrow_forwardThe 200-mm-radius disk rolls without sliding on the surface shown. Knowing that the distance BG is 160 mm and that at the instant shown the disk has an angular velocity of 5.50 rad/s counterclockwise and an angular acceleration of 7.00 rad/s² clockwise, determine the acceleration of A. A 730 mm 200 mm Barrow_forwardThe 200-mm-radius disk rolls without sliding on the surface shown. Knowing that the distance BG is 160 mm and that at the instant shown the disk has an angular velocity of 8.6 rad/s counterclockwise and an angular acceleration of 2.3 rad/s2 clockwise, determine the acceleration of A. 800 mm The acceleration of A is 11.55 200 mm B m/s²_arrow_forward
- 5.- Knowing that at the instant shown bar AB has an angular velocity of 4 rad/s and an angular acceleration of 2 rad/s?, both clockwise, determine the angular acceleration (a) of bar BD, (b) of bar DE by using the vector approach. 100 mm 175 mm - B A 200 mm 75 mm D Earrow_forwardB. In Fig. below; rod AB rotates about an axis through A and is connected to block D by a flexible and inextensible cable. Determine the linear velocity of block D when 0 = tan ( 3 /4 ), and the angular velocity of AB is 2.5 rad / sec counterclockwise. Fig.2.B B 1.5m 25marrow_forwardThe bucket of a backhoe is the element AB of the four-bar linkage system ABCD. Assume that the points A and D are fixed and that the bucket rotates with a constant angular velocity WAB = 0.25 rad/s. In addition, suppose that, at the instant shown, point B is aligned vertically with point A, and C is aligned horizontally with B. Determine the acceleration of point C at the instant shown along with the angular acceleration of the elements BC and CD. Let h= 0.66 ft, e= 0-46 ft, l= 0.9 ft, and w= 1.0 ft.arrow_forward
- If crank AB rotates with an angular velocity of wAB angular acceleration a AB = 6 rad/s? at the instant shown, determine: 1.1. The angular velocity of rod BC and the velocity of the slider block 1.2. The angular acceleration of rod BC and the linear acceleration of = 5 rad/s and an 0.5 m 0,3 m B 60° 30° WAB slider Block. 1.3. Locate the instantaneous center (IC) of the rod BC. CABarrow_forwardArm AB has a constant angular velocity of 16 rad/s counterclockwise. At the instant when 0 = 0, determine the acceleration (a) of collar D. (b) of the midpoint G of bar BD. 3 in. A B 10 in. 6 in.arrow_forwardThe combined pulley shown has two cables wound around it at different diameters and fastened to point A and block E, respectively. Member ABOCD rotates counter clockwise to lift block E. If the total acceleration of point D is 5 in/s²Z45° at the instant shown, determine: a) the angular velocity of member ABCD3; b) the angular acceleration of member ABCD; c) the velocity of block E. Ø5" F Ø3" 5" B C, E 4" 8" 4"arrow_forward
- Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. For a 5-m steel beam AE, the acceleration of point A is 2.5 m/s² downward and the angular acceleration of the beam is 1.5 rad/s2 counterclockwise. Knowing that at the instant considered the angular velocity of the beam is zero, determine the acceleration of cable B and cable D. A -1.5 m- B Determine the acceleration of cable B The acceleration of cable Bis 2 m 1.375 5 m/s2. D -1.5 m- Earrow_forwardBar AB of the for link mechanism rotates with a constant angular veleocity of 10 rad/s. For the position shown, determine: a) tHE ANGULAR VELOCITIES of bars BC and CD b) the angular accelerations of bars BC and CDarrow_forwardKnowing that at the instant shown crank BC has a constant angular velocity of 90 rpm counterclockwise, determine the acceleration (a) of point A, (b) point D. D 100 mm 200 mm B 200 mmarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY