Concept explainers
(a)
Angular acceleration of bar BD.
Answer to Problem 15.134P
The angular acceleration of bar BD is
Explanation of Solution
Given information:
Angular velocity of bar AB is
Angular acceleration of bar AB is
The absolute value of point A
The relative velocity of A with respect to B is defined as
The absolute acceleration of point B is defined as:
The tangential acceleration is defined as:
The normal acceleration is defined as:
In above equations
Calculation:
Position vector of B relative to A:
Position vector of D relative to B:
Position vector of D relative to E:
For bar AB
Velocity of point B
For bar BD:
Velocity of point D:
For bar DE:
Velocity of point D:
Equate above equations:
Equate components:
Therefore:
For bar AB:
Acceleration of point B:
We know that:
Therefore:
For bar BD:
Acceleration of point D:
Substitute:
Therefore:
For bar DE:
Acceleration of point D:
Substitute:
Therefore:
Equate above equations:
Equate components:
Solve above equations:
Conclusion:
The angular acceleration of bar BD is
(b)
Angular acceleration of bar DE
Answer to Problem 15.134P
The angular acceleration of bar DE is
Explanation of Solution
Given information:
Angular velocity of bar AB is
Angular acceleration of bar AB is
The absolute value of point A
The relative velocity of A with respect to B is defined as
The absolute acceleration of point B is defined as
The tangential acceleration is defined as
The normal acceleration is defined as
In above equations
Calculation:
According to sub part a
Acceleration of point D for bar BD
Acceleration of point D for bar DE
Equate above equations
Equate components
Therefore
Conclusion:
The angular acceleration of bar DE is
Want to see more full solutions like this?
Chapter 15 Solutions
VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
- The lower portion of a fire ladder (OA) rotates about the hinge at O at a rate of 0.05 rad/s. The angular acceleration of OA is 0.04 rad/s?. At the same time, the upper portion (AB) extends out from the lower portion at a velocity of 0.4 m/s and an acceleration of 0.1 m/s?. The length of OA is 6 m and the length of AB is 2m. a) Calculate the velocity and acceleration of point B with respect to O. Keep your work in polar coordinates. b) Transform your solutions from Part (a) to Cartesian coordinates if 0 = T1/6. A 36°F Clear Type here to search 53arrow_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_forwardIf 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_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_forwardAdvanced Applied Mathematics - Circular Motion 1. When an airplane touches down at 1 = 0, a stationary wheel is subjected to a constant angu- lar acceleration a = 110 rad/s until / = 1 s. (a) What is the wheel's angular velocity at t = 1 s? (b) At 1 = 0, the angle 0 = 0. Determine 9 in radians and in revolutions at / = 1 s. 2. A small box B of mass mkg is placed on a rough horizontal rotating disc. B is metres from the centre of rotation as shown in Fig. 1 below. The coefficient of friction between the disc and B is u. Find, in terms of u, r and g, the maximum speed v that can be given to B without it slipping. 3. One end of a light inextensible string of length L metres is attached to a fixed point C. A small brass hall Roarrow_forwardRequired 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_forward
- A rigid link PQ of length 2 m rotates about the pinned end Qwith a constant angular acceleration of 12 rad/s2. When the angular velocity of the link is 4 rad/s, the magnitude of the resultant acceleration (in m/s²) of the end Pisarrow_forwardQ1: The crank OA of the offset sli der-crank mech anism rotates with a constant clockwise angul ar velocity o, = 12 rad/s. For the position shown: 1.1 The angular acceleration of link AB and the acceleration of B. 1.2 Locate the instantane ous center of zero velocity (IC) for the link AB. 60° 45° B OA = 75 mm %3D 15° AB = 225 mmarrow_forwardThe elliptical exercise machine shown below has fixed axes of rotation at points A and E. Knowing that at the instant shown the flywheel AB has a constant angular velocity of 6 rad/s clockwise, determine the acceleration of point D. Solve this problem, then assuming the ease of starting the elliptical moving is proportional to the angular velocity (app) and using only the equations below plus geometry, how would you redesign the machine to minimize the effort needed to start the elliptical moving. Be sure to resolve the problem based on your redesign to show that the effort would be lowered and estimate the percent change in effort. aв = a +ax TB/A - W²TB/A VB = VA+WXTB/A 0.2 m 1.2 m 0.09 m 0.12 m 0.6 m 0.8 marrow_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