Concept explainers
Knowing that at the instant shown bar AB has a constant angular velocity of 4 rad/s clockwise, determine the angular acceleration (a) of bar BD, (b) of bar DE.
(a)
The angular acceleration of bar
Answer to Problem 15.132P
The angular acceleration of bar
Explanation of Solution
Given information:
The constant angular velocity of bar
Write the expression of position vector of a point.
Here, the coordinate in
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 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
Here, the Equation (IX) is the cross product of two vector, now change it in determinant form.
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.
Compare the term of
Compare the term of
Substitute
Substitute
Here, the Equation (XIII) is the cross product of two vector, now change it in determinant form.
Substitute
Here, the Equation (XIV) 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 15.132P
Explanation of Solution
Calculation:
Compare the terms of
Conclusion:
The angular acceleration of bar
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics for Engineers: Dynamics
- The 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_forwardThe instant shown, bar AB has an angular velocity of 6.5 rad/s and an angular acceleration of 4 rad/s², both clockwise. 200 mm B 75 mm D 175 mm 100 mm A E Determine the angular acceleration of bar BD by using the vector approach. (You must provide an answer before moving to the next part.) The angular acceleration of bar BD is rad/s² clockwise.arrow_forward3. The solid cylinder rotates around z-axis at constant angular velocity. At the instant shown, point P on the rim of the cylinder is at an angle of 0 = 25° w.r.t. x-axis and has a velocity in the x direction of vx = 5.3 ft/s, determine the angular velocity, , of the disk, and the acceleration, a, of point P, express the acceleration in vector form in terms of its x and y components. The radius of the cylinder is r = 6 in. a = -285.07762-132.934j [ft/sarrow_forward
- Arm 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_forwardAt the shown position OA is horizontal and is rotating counterclockwise with constant angular speed of 9 rad/s. Rod AB is 200 mm long, answer the following: 100 mm 9 rad/s The angular velocity of AB, @AR The angular acceleration of AB, aAR 80 mm The acceleration of B, agarrow_forwardDrum C is connected to collar A through Bar AB. Point B is directly to the right of center of drum C. The velocity of B is 3 m/s downward while velocity of A is 3 m/s to the left. Bar AB has an angular velocity of 2.83 rad/s. If Drum C in a given instant has an angular velocity of 2.50 rad/s CW is then given an angular acceleration of 1.800 rad/s2 CW what is the magnitude of acceleration of point B?arrow_forward
- The 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_forwardBoth 15-cm-radius wheels roll without slipping on the horizontal surface. Knowing that the distance AD is 12.5 cm, the distance BE is 10 cm, that D has a velocity of 30 cm/s to the right and acceleration of E is 60 cm/s? to the left, determine the angular velocity and angular acceleration of link AB, angular velocity and angular acceleration of both wheels. Also determine the acceleration of point C. | 30 y Wheel 1 45 cm Wheel 2 /A 15cm 10 cm VD=30 cm/s B aE=60 cm/s2 15 cm 12.5 cmarrow_forwardAt the instant shown, the velocity of collar A is 0.4 m/s to the right and the velocity of collar B is 1 m/s to the left. Determine (a) the angular velocity of bar AD, (b) the angular velocity of bar BD, (c) the velocity of point D.arrow_forward
- Consider the pulley system A and B. Pulley A has a radius of 1.5 m while pulley B has a radius of 0.375 m. Pulley B has an angular acceleration of 3.5 rad/s2 clockwise. 1. Which is the approximate direction of acceleration of point E? 2. Which of the following is closest to the magnitude of the angular acceleration of pulley A?arrow_forward2) At the instant given, it is known that the angular velocity of rod AB is 20 rad/s clockwise. By use of Cartesian vector form, determine (a) the angular velocity of rod BD, (b) the velocity of the point D. 0.2 m 0.25 m D 0.2 m E -0.6 m 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 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_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