(a)
The angular momentum of the assembly about point
Answer to Problem 18.15P
The angular momentum of the assembly about point
Explanation of Solution
Given information:
The mass of each L-shaped arm is
The below figure represents x’, y’, and z’ axis parallel to the x, y, and z axis.
Figure (1)
Write the expression for angular velocity in x’-direction.
Write the expression for angular velocity in y’-direction.
Write the expression for mass of each segment of arm
Here,
Write the expression for angular velocity in z-direction.
Here, speed of assembly is
Write the expression for moment of inertia for part (1) in x-z direction
Here mass moment of inertia along x-y direction is
Write the expression for moment of inertia for part (1) in y-z direction.
Here mass moment of inertia along y-z direction is
Write the expression for moment of inertia for part (1) in z direction
Here mass moment of inertia along z direction is
Write the expression for moment of inertia for part (2) in x-z direction.
Here, mass moment of inertia along x-y direction is
Write the expression for moment of inertia for part (2) in y-z direction.
Here mass moment of inertia along y-z direction is
Write the expression for moment of inertia for part (2) in z direction.
Here mass moment of inertia along z direction is
Write the expression for moment of inertia for part (3) in x-z direction.
Here, mass moment of inertia along x-z direction is
Write the expression for moment of inertia for part (3) in y-z direction.
Here, mass moment of inertia along y-z direction is
Write the expression for moment of inertia for part (3) in z direction.
Here mass moment of inertia along z direction is
Write the expression for moment of inertia for part (4) x-z direction.
Here, mass moment of inertia along x-y direction is
Write the expression for moment of inertia for part (4) y-z direction.
Here, mass moment of inertia along y-z direction is
Write the expression for moment of inertia for part (4) z direction.
Here mass moment of inertia along z direction is
Write the expression for total mass moment of inertia in x-y direction.
Write the expression for total mass moment of inertia in y-z direction.
Write the expression for total mass moment of inertia in z direction.
Substitute
Substitute
Substitute
Write the expression for angular momentum in x-z direction.
Substitute
Write the expression for angular momentum in y-z direction.
Substitute
Write the expression for angular momentum in z direction.
Substitute
Write the expression for
Substitute,
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus angular momentum of the assembly about point
(b)
The angle formed by
Answer to Problem 18.15P
The angle formed by
Explanation of Solution
Given information Write the expression for the magnitude of angular momentum in about assembly A
Write the Expression for angle formed by
Calculation:
Substitute
Substitute
Conclusion:
Thus angle formed by
Want to see more full solutions like this?
Chapter 18 Solutions
VECTOR MECH...,DYNAMICS(LOOSE)-W/ACCESS
- Can you solve it analytically using laplace transforms and with Matlab code as well please. Thank You.arrow_forwardQ11. Determine the magnitude of the reaction force at C. 1.5 m a) 4 KN D b) 6.5 kN c) 8 kN d) e) 11.3 KN 20 kN -1.5 m- C 4 kN -1.5 m B Mechanical engineering, No Chatgpt.arrow_forwardplease help with this practice problem(not a graded assignment, this is a practice exam), and please explain how to use sohcahtoaarrow_forward
- Solve this problem and show all of the workarrow_forwardSolve this problem and show all of the workarrow_forwardaversity of Baoyion aculty of Engineering-AIMusyab Automobile Eng. Dep. Year: 2022-2023, st Course, 1st Attempt Stage: 3rd Subject: Heat Transfer I Date: 2023\01\23- Monday Time: 3 Hours Q4: A thick slab of copper initially at a uniform temperature of 20°C is suddenly exposed to radiation at one surface such that the net heat flux is maintained at a constant value of 3×105 W/m². Using the explicit finite-difference techniques with a space increment of Ax = = 75 mm, determine the temperature at the irradiated surface and at an interior point that is 150 mm from the surface after 2 min have elapsed. Q5: (12.5 M) A) A steel bar 2.5 cm square and 7.5 cm long is initially at a temperature of 250°C. It is immersed in a tank of oil maintained at 30°C. The heat-transfer coefficient is 570 W/m². C. Calculate the temperature in the center of the bar after 3 min. B) Air at 90°C and atmospheric pressure flows over a horizontal flat plate at 60 m/s. The plate is 60 cm square and is maintained at a…arrow_forward
- University of Baby on Faculty of Engineering-AIMusyab Automobile Eng. Dep. Year: 2022-2023. 1 Course, 1" Attempt Stage 3 Subject Heat Transfer I Date: 2023 01 23- Monday Time: 3 Hours Notes: Q1: • • Answer four questions only Use Troles and Appendices A) A flat wall is exposed to an environmental temperature of 38°C. The wall is covered with a layer of insulation 2.5 cm thick whose thermal conductivity is 1.4 W/m. C, and the temperature of the wall on the inside of the insulation is 315°C. The wall loses heat to the environment by convection. Compute the value of the convection heat-transfer coefficient that must be maintained on the outer surface of the insulation to ensure that the outer-surface temperature does not exceed 41°C. B) A vertical square plate, 30 cm on a side, is maintained at 50°C and exposed to room air at 20°C. The surface emissivity is 0.8. Calculate the total heat lost by both sides of the plate. (12.5 M) Q2: An aluminum fin 1.5 mm thick is placed on a circular tube…arrow_forwardSolve using graphical method and analytical method, only expert should solvearrow_forwardSolve this and show all of the workarrow_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