Explanation Given information: The weight of the plate is 10 lb , the rotational velocity is 8 rad / s and the couple of moment is ( 0.75 ft ⋅ lb ) j . The below figure represent the schematic diagram of the system. Figure-(1) Write the expression of angular momentum of the system about point A . H A = − I x y ω i + I y ω j − I y z ω k ......... (I) Here, the angular momentum about point A in x y direction is I x y , the angular momentum about point A in y direction is I y , the angular momentum about point A in y z direction is I y z , the angular velocity is ω , the unit vector along the x ′ axis is i ′ , the unit vector along the y ′ axis is j ′ and the unit vector along the z ′ axis is k ′ . Write the expression of angular momentum about point A in x y direction. I x y = m A ( I x y ) area ......... (II) Here, the mass is m , the area is A and the area momentum about point A in x y direction is ( I x y ) area . Write the expression of area. A = 1 2 b h Here, the breadth is b and the height is h . Write the expression of area momentum about point A in x y direction. ( I x y ) area = 1 24 b 2 h 2 Substitute 1 2 b h for A and 1 24 b 2 h 2 for ( I x y ) area in Equation (II). I x y = m ( 1 2 b h ) ( 1 24 b 2 h 2 ) = m b h 12 Write the expression of angular momentum about point A in y direction. I y = m A ( I y ) area ......... (III) Here, the area momentum about point A in y direction is ( I y ) area . Write the expression of area momentum about point A in y direction. ( I y ) area = 1 12 b 3 h Substitute 1 2 b h for A and for ( I y ) area in Equation (III). I y = m ( 1 2 b h ) ( 1 12 b 3 h ) = m b 2 6 Write the expression of angular momentum about point A in y z direction. I y z = 0 Substitute 0 for I y z , m b 2 6 for I y and m b h 12 for I x y in Equation (I). H A = − ( m b h 12 ) ω i + ( m b 2 6 ) ω j − ( 0 ) ω k = − ( m b h 12 ) ω i + ( m b 2 6 ) ω j Write the expression of moment about A . M A = M 0 j + ( h j ) × ( B x i + B z k ) = M 0 j + ( h j ) × ( B x i ) + ( h j ) × B z k = M 0 j + − h B x k + h B z i = M 0 j + h B z i − h B x k Here, the force at point B in x direction is B x , the force at point B in z direction is B z and the height is h To determine (b) The dynamic reactions at A . The dynamic reactions at B .

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 18.2, Problem 18.72P

To determine

(a)

The angular acceleration of the assembly.

To determine

(b)

The dynamic reactions at A.

The dynamic reactions at B.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 18.2, Problem 18.71P

Chapter 18.2, Problem 18.73P

Students have asked these similar questions

A half-cylinder with mass m and radius r is released from rest in the position shown. Knowing that the half-cylinder rolls without sliding, determine (a ) its angular velocity after it has rolled through 90°, (b ) the reaction at the horizontal surface at the same instant. [Hint: Not that GO = 4r/3 π and that, by the parallel-axis theorem,

If the earth were a sphere, the gravitational attraction of the sun, moon, and planets would at all times be equivalent to a single force R acting at the mass center of the earth. However, the earth is actually an oblate spheroid and the gravitational system acting on the earth is equivalent to a force R and a couple M. Knowing that the effect of the couple M is to cause the axis of the earth to precess about the axis GA at the rate of one revolution in 25 800 years, determine the average magnitude of the couple M applied to the earth. Assume that the average density of the earth is 5.51 g/cm 3 , that the average radius of the earth is 6370 km, and that ( Note: This forced precession is known as the precession of the equinoxes and is not to be confused with the free precession discussed in Prob. 18.123.)

A 5.32-kg disk A of radius 0.445 m initially rotating counter-clockwise at 436 rev/min is engaged with a 6.72-kg disk B of radius 0.275 m initially rotating clockwise at 528 rev/min, where the moment of inertia of a disk is given as I = ½ mi?. Determine their combined angular speed (in rpm) and direction of rotation after the meshing of the two disks. Remember to show clearly the equations that you use!!'

Chapter 18 Solutions

Vector Mechanics For Engineers

Ch. 18.1 - Prob. 18.1P Ch. 18.1 - Prob. 18.2P Ch. 18.1 - Prob. 18.3P Ch. 18.1 - A homogeneous disk of weight W=6 lb rotates at the...Ch. 18.1 - Prob. 18.5P Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Solve Prob. 18.6, assuming that the solid...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

(a) The angular acceleration of the assembly.

Solution Summary: The following figure represent the schematic diagram of the system.