Concept explainers
In Prob. 15.10, determine the velocity and acceleration of corner B, assuming that the angular velocity is 9 rad/s and increases at the rate of 45 rad/s2.
The velocity and acceleration of corner3
Answer to Problem 15.11P
The velocity of corner
The acceleration of corner
Explanation of Solution
Given information:
The angular velocity is
Expression of position vector of point
Here, the distance in
Expression of position vector of point
Here, the distance in
Expression of rotation vector along the line
Here, the angular velocity is
Expression of unit vector of point
Here, the magnitude of position vector of point
Expression of magnitude of position vector of point
Here, the distance in
Expression of velocity of point
Here, the of rotation vector along the line
Expression of angular acceleration vector
Here, the angular acceleration is
Expression of acceleration of corner
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Here, the Equation (IX) is a cross product of two vector now change it in determinant form.
Substitute
Substitute
Here, the cross product of two vector, now change it in determinant form.
Conclusion:
The velocity of corner
The acceleration of corner
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics for Engineers: Dynamics
- QUESTION 1 The slider block C moves at 7.5 m/s down the inclined groove. 1- Determine the angular velocity of link AB at the instant shown measured clockwise. 2- Determine the angular velocity of link BC at the instant shown measured clockwise. -2 m- 45 2m a. 2.65 , -9.34 Cb.9.34 , -9.34 Cc.-2.65 , 9.34 Cd.2.65 , -2.65 B.arrow_forward5.- 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_forwardThe angular velocity of the link AB is 2.7 rad/s clockwise, determine the velocity of collar D.arrow_forward
- Section D QU The double gear shown rolls on the stationary lower rack; the vclocity of its center A is 1.6 m/s directed to the right. Determine the angular velocity of the gear if r1-175 mm and r2-125 mm O -9.1428 rad/s O 10.3568 rad/s O 7.9428 rad/s O 11.8365 rad/s Q6/ The link OA has a constant clockwise angular velocity of 2000 rpm. For the 97F Sunny LATITUDE 12 F10 ドブ 144 & 6 Y ! DI F 1 GY マ C V B Y M Alt 31arrow_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_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_forward
- The collar C as shown in figure O is moving downward with a velocity of 2 m/s. 1. Determine the angular velocity of CB a. 9 rad/sb. 15 rad/sc. 10 rad/sd. 12 rad/s2. Determine the angular velocity of AB a. 9 rad/sb. 15 rad/sc. 10 rad/sd. 12 rad/sarrow_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_forward3. Cables at A and B are tightly wrapped around the rim and hub of the pulley. The cables are given upward velocities at A and B of 4 m/'s and 3 m/s, respectively. What is the angular velocity of the pulley and the velocity of the center O? B. A. B. 90 mm Hint: One equation that I wrote to solve this was yo = yA – RO 180 mm,arrow_forward
- The 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 of5.50rad/s counterclockwise and an angular acceleration of 7.00 rad/s² clockwise, determine the acceleration of A. A 730 mm 200 mm Barrow_forwardThe outer gear A rotates with an angular velocity of 6 rad/s counterclockwise. Knowing that the angular velocity of the intermediate gear B is 3 rad/s clockwise, determine: 1. The angular velocity of the arm ABC 2. The angular velocity of the outer gear C. 5 in. 10 in. C B -15 in.- -15 in.- Select one: O A. arm = 3 rad/s (CW); and @c = 1.5 rad/s (CW) O B. Warm = 5 rad/s (CW); and @c = 3 rad/s (CW) O C.o arm = 0 rad/s ; and @c = 1.5 rad/s (CCW) O D. warm = 1 rad/s (CW); and wc = 0 rad/sarrow_forwardThe angular velocity of the link AB is 2.7 rad/s clockwise, determine (a) the angular velocity of linkBD.arrow_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