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
- Knowing that at the instant shown the angular velocity of rod AB is 15 rad/s clockwise, write down the equation of velocity of point B relative to point A. -V_Bi=(-15k)x(-0.2j) +V_Bj=V_Ai-(15k) x (0.6i+0.25j) -V_Bi=V_A+(-15k)x(0.2j) +V_Bj=V_Ai-(omega_BDk) x (-0.6i-0.25j)arrow_forwardA painter is half way up a 10-m ladder when the bottom starts sliding out from under him. Knowing that point A has a velocity vA = 2 m/s directed to the left when 0= 60°, determine (a) the angular velocity of the ladder, (b) the velocity of the painter.arrow_forwardIn order to uncoil electrical wire from a 0.6-m-radius spool fixed to a truck, a worker drives to the left with a speed of vA = 5 m/s. At the same time, a second worker holds the cable as he walks to the right with a speed of vB = 3 m/s. Knowing that at the instant shown the thickness of wire on the spool is 40 mm, determine (a) the instantaneous center of rotation of the spool, (b) the velocity of point D on the inside of the spool.arrow_forward
- A circular plate of 120 mm radius is supported by two bearings A and B as shown. The plate rotates about the rod joining A and B with a constant angular velocity of 26 rad/s. Knowing that, at the instant considered, the velocity of Point C is directed to the right, determine the velocity and acceleration of Point E.arrow_forwardA 3-in.-radius drum is rigidly attached to a 5-in.-radius drum as shown. One of the drums rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that at the instant shown. point A has a velocity of 5.75 in./s and an acceleration of 19 in./s2, both directed to the right, determine the accelerations of points A, B, and C of the drums. a) The accelerations of point B is _ upward? b) The accelerations of point A is _ and _? (magnitude and direction) c) The accelerations of point C is _ and _? (magnitude and direction)arrow_forwardA series of small machine components being moved by a conveyor belt pass over a 120-mm-radius idler pulley. At the instant shown, the angular velocity of the idler pulley is 4 rad/s clockwise. Determine the angular acceleration of the pulley for which the magnitude of the total acceleration of the machine component at B is 2400 mm/s2.arrow_forward
- Consider that at the instant shown, bar AB of the mechanical system below has a angular velocity (wAB) counterclockwise at 5 rad/s and an angular acceleration (alphaAB)counterclockwise 2 rad/s².The length of bar AB is 0.4 m and the length of bar BC is 1 m. For the instant shown, and using a "Analysis of Relative Motion", determine: (a) the speed of point B (b) angular velocity of connecting bar BC (c) the speed of point C (d) the acceleration of point B (d) the acceleration of point Carrow_forwardIn Prob. 15.14, determine the velocity and acceleration of point E , assuming that the angular velocity is 26 rad/s and increases at the rate of 65 rad/s2.Reference to Problem 15.14:A circular plate of 120-mm radius is supported by two bearings A and B as shown. The plate rotates about the rod joining A and B with a constant angular velocity of 26 rad/s. Knowing that, at the instant considered, the velocity of point C is directed to the right, determine the velocity and acceleration of point E.arrow_forwardA helicopter moves horizontally in the x direction at a speed of 120 mi/h. Knowing that the main blades rotate clockwise when viewed from above with an angular velocity of 180 rpm, determine the instantaneous axis of rotation of the main blades.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