
Concept explainers
In Prob. 15.199, determine (a) the common angular acceleration of gears A and B, (b) the acceleration of the tooth of gear A that is in contact with gear C at point 1.

(a)
The common angular acceleration of the gears
Answer to Problem 15.200P
The common angular acceleration of the gears
Explanation of Solution
Given Information:
The angular velocity of the gear
Draw the schematic diagram of the given system.
Figure-(1)
Write the expression for the velocity of point 1.
Here, the angular velocity of the gear
Write the expression for the velocity of point 1 when gear
Here, the angular velocity of the shaft unit carries gear
Write the expression for the velocity of point 2.
Here, the angular velocity of the gear
Write the expression for the velocity of point 2 when gear
Write the expression for the angular velocity of the inclined shaft unit which carries gear
Here, the angular velocity of the shaft in x- direction is
Draw the diagram to show the motion of the shaft is
Figure-(2)
Write the expression for the velocity of point
Here, the position vector at point
Write the expression for the velocity at point
Here, the angular velocity of shaft
Write the expression for the common angular acceleration of the gear
Calculation:
Consider the unit vector along
From Figure-(1) the coordinate of the point 1 at the intersection of the gears
From Figure-(1) the coordinate of the point 2 at the intersection of the gears
Since, the shaft
Substitute
Substitute
Substitute
Compare the terms along the x- direction in Equation (X).
Compare the terms along the z- direction in Equation (X).
Since, the shaft
Substitute
Substitute
Substitute
Compare the terms along the z- direction in Equation (X).
Substitute
Substitute
Substitute
From Figure-(2) the coordinate of the point
Substitute
Substitute
Substitute
Substitute
Conclusion:
The common angular acceleration of the gear

(b)
The acceleration of the tooth of the gear
Answer to Problem 15.200P
The acceleration of the tooth of the gear
Explanation of Solution
Write the expression for the acceleration of the gear
Calculation:
Substitute
Conclusion:
The acceleration of the tooth of the gear
Want to see more full solutions like this?
Chapter 15 Solutions
Vector Mechanics for Engineers: Dynamics
- PROBLEM 3.46 The solid cylindrical rod BC of length L = 600 mm is attached to the rigid lever AB of length a = 380 mm and to the support at C. When a 500 N force P is applied at A, design specifications require that the displacement of A not exceed 25 mm when a 500 N force P is applied at A For the material indicated determine the required diameter of the rod. Aluminium: Tall = 65 MPa, G = 27 GPa. Aarrow_forwardFind the equivalent mass of the rocker arm assembly with respect to the x coordinate. k₁ mi m2 k₁arrow_forward2. Figure below shows a U-tube manometer open at both ends and containing a column of liquid mercury of length l and specific weight y. Considering a small displacement x of the manometer meniscus from its equilibrium position (or datum), determine the equivalent spring constant associated with the restoring force. Datum Area, Aarrow_forward
- 1. The consequences of a head-on collision of two automobiles can be studied by considering the impact of the automobile on a barrier, as shown in figure below. Construct a mathematical model (i.e., draw the diagram) by considering the masses of the automobile body, engine, transmission, and suspension and the elasticity of the bumpers, radiator, sheet metal body, driveline, and engine mounts.arrow_forward3.) 15.40 – Collar B moves up at constant velocity vB = 1.5 m/s. Rod AB has length = 1.2 m. The incline is at angle = 25°. Compute an expression for the angular velocity of rod AB, ė and the velocity of end A of the rod (✓✓) as a function of v₂,1,0,0. Then compute numerical answers for ȧ & y_ with 0 = 50°.arrow_forward2.) 15.12 The assembly shown consists of the straight rod ABC which passes through and is welded to the grectangular plate DEFH. The assembly rotates about the axis AC with a constant angular velocity of 9 rad/s. Knowing that the motion when viewed from C is counterclockwise, determine the velocity and acceleration of corner F.arrow_forward
- 500 Q3: The attachment shown in Fig.3 is made of 1040 HR. The static force is 30 kN. Specify the weldment (give the pattern, electrode number, type of weld, length of weld, and leg size). Fig. 3 All dimension in mm 30 kN 100 (10 Marks)arrow_forward(read image) (answer given)arrow_forwardA cylinder and a disk are used as pulleys, as shown in the figure. Using the data given in the figure, if a body of mass m = 3 kg is released from rest after falling a height h 1.5 m, find: a) The velocity of the body. b) The angular velocity of the disk. c) The number of revolutions the cylinder has made. T₁ F Rd = 0.2 m md = 2 kg T T₂1 Rc = 0.4 m mc = 5 kg ☐ m = 3 kgarrow_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





