
(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 Mechanics For Engineers
- 25 mm Brass core E = 105 GPa 0 = 20.9 x 10 °C PROBLEM 2.49 The aluminum shell is fully bonded to the brass core and the assembly is unstressed at a temperature of 15°C. Considering only axial deformations, determine the stress in the aluminum when the temperature reaches 195°C. 60 mm Aluminum shell E = 70 GPa a = 23.6 × 10°Carrow_forwardThis is an old practice exam. The answers are OAB = 19.10 ksi OBC = 2.228 ksi OCD = −2.865 ksi v = 0.2792delta Ltot = 0.01585 in (increase) but whyarrow_forwardA random poly(styrene-butadiene) copoly- mer has a number-average molecular weight of 350,000 g/mol and a degree of polymerization of 5000. Compute the fraction of styrene and buta- diene repeat units in this copolymer. H H | | -C-C- 방 Harrow_forward
- Design and assemble on the fluidsim (or a draft) the Hydraulic Drive Circuit, with the following characteristics: (a) Sequential operation, pressure, for the advance and return of the cylinders (according to the proper operation for the device) controlled by a directional 4x3 way, closed center; (b) Speed control for the cylinders, according to the load signal; (c) Pressure counterbalance for cylinder A, in order to compensate for the weight of the assembly.arrow_forwardThis is an old exam practice question. The answer is Pmax = 218.8 kN normal stress governs but why?arrow_forwardMoist air initially at T₁ = 140°C, p₁ = 4 bar, and p₁ = 50% is contained in a 2.0-m³ closed, rigid tank. The tank contents are cooled to T₂ 35°C. Step 1 Determine the temperature at which condensation begins, in °C.arrow_forward
- Air at T₁ = 24°C, p₁ = 1 bar, 50% relative humidity enters an insulated chamber operating at steady state with a mass flow rate of 3 kg/min and mixes with a saturated moist air stream entering at T2=7°C, p₂ = 1 bar. A single mixed stream exits at T3-17°C, p3=1 bar. Neglect kinetic and potential energy effectsarrow_forwardHand calculation of cooling loadarrow_forwardAn HEV has a 24kW battery. How many miles can it go on electricity alone at 40 mph on a flat straight road with no headwind? Assume the rolling resistance factor is 0.018 and the Coefficient of Drag (aerodynamic) is 0.29 the frontal area is 2.25m^2 and the vehicle weighs 1618 kg.arrow_forward
- As shown in the figure below, moist air at T₁ = 36°C, 1 bar, and 35% relative humidity enters a heat exchanger operating at steady state with a volumetric flow rate of 10 m³/min and is cooled at constant pressure to 22°C. Ignoring kinetic and potential energy effects, determine: (a) the dew point temperature at the inlet, in °C. (b) the mass flow rate of moist air at the exit, in kg/min. (c) the relative humidity at the exit. (d) the rate of heat transfer from the moist air stream, in kW. (AV)1, T1 P₁ = 1 bar 11 = 35% 120 T₂=22°C P2 = 1 bararrow_forwardThe inside temperature of a wall in a dwelling is 19°C. If the air in the room is at 21°C, what is the maximum relative humidity, in percent, the air can have before condensation occurs on the wall?arrow_forwardThe inside temperature of a wall in a dwelling is 19°C. If the air in the room is at 21°C, what is the maximum relative humidity, in percent, the air can have before condensation occurs on the wall?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





