
Concept explainers
(a)
Find the principal mass moment of inertia at the origin.
(a)

Answer to Problem 9.181P
The principal mass moment of inertia at the origin is
Explanation of Solution
Calculation:
Refer to problem 9.145 and 9.149.
Substitute the values of
Solve the above Equation.
Thus, the principal mass moment of inertia at the origin is
(b)
Find the principal axis of inertia at the origin.
(b)

Answer to Problem 9.181P
The principal axis of inertia at the origin for
The principal axis of inertia at the origin for
The principal axis of inertia at the origin for
Explanation of Solution
Calculation:
Use Equation 9.54 and 9.57 to find the direction cosines
For
Use Equation 9.54a and 9.54b.
Substitute
Simplifying,
Solving the Equations (1) and (2) for
Substitute into
Substitute into Equation 9.57:
Thus, the principal axis of inertia at the origin for
For
Use Equation 9.54a and 9.54b.
Substitute
Simplifying
Solving Equations (3) and (4) for
Substitute
Substitute into Equation 9.57:
Thus, the principal axis of inertia at the origin for
For
Use Equation 9.54a and 9.54b.
Substitute
Simplifying
Solving Equations (5) and (6) for
Substitute
Substitute into Equation 9.57:
Find the direction cosines corresponding to the labelled axis, take the negative root of
Thus, the principal axis of inertia at the origin is
Sketch the orientation of the principal axis to the
Refer to Figure 1.
Principal axis 3 has been labelled so that the principle axes form a right handed set.
Want to see more full solutions like this?
Chapter 9 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
- 2. 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_forward1. 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_forward
- 2.) 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_forward500 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_forward
- A 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(read image) (answer given)arrow_forward11-5. Compute all the dimensional changes for the steel bar when subjected to the loads shown. The proportional limit of the steel is 230 MPa. 265 kN 100 mm 600 kN 25 mm thickness X Z 600 kN 450 mm E=207×103 MPa; μ= 0.25 265 kNarrow_forward
- T₁ F Rd = 0.2 m md = 2 kg T₂ Tz1 Rc = 0.4 m mc = 5 kg m = 3 kgarrow_forward2. Find a basis of solutions by the Frobenius method. Try to identify the series as expansions of known functions. (x + 2)²y" + (x + 2)y' - y = 0 ; Hint: Let: z = x+2arrow_forward1. Find a power series solution in powers of x. y" - y' + x²y = 0arrow_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





