Explanation Given information: The mass of the uniform rod is m , the length of the shaft is 2 b and the angular velocity is ω Write the expression of moment of inertia of the uniform rod about y ′ axes. I y ′ = 1 3 m b 2 Here, the mass of the rod is m and the half length of the rod is b . Write the expression of moment of inertia of the uniform rod about z ′ axes. I z ′ = 1 3 m b 2 Write the expression of moment of inertia of the uniform rod about x ′ axes. I x ′ = 0 Write the expression of angular velocity of the shaft about x ′ axes. ω x ′ = − ω sin β Here, the angular velocity of the shaft is ω and the angle between x ′ and x axes is β . Write the expression of angular velocity of the shaft about y ′ axes. ω y ′ = ω cos β Write the expression of angular velocity of the shaft about z ′ axes. ω z ′ = 0 Write the expression of angular momentum of the system about point G . H G = I x ′ ω x ′ i ′ + I y ′ ω y ′ j ′ + I z ′ ω z ′ k ′ ......... (I) Here, 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 ′ . Substitute 0 for I x ′ , 1 3 m b 2 for I y ′ , 1 3 m b 2 for I z ′ , − ω sin β for ω x ′ , ω cos β for ω y ′ and 0 for ω z ′ in Equation (I). H G = ( 0 ) ( − ω sin β ) i ′ + ( 1 3 m b 2 ) ( ω cos β ) j ′ + ( 1 3 m b 2 ) ( 0 ) k ′ = 0 + ( 1 3 m b 2 ) ( ω cos β ) j ′ + 0 = ( 1 3 m b 2 ) ( ω cos β ) j ′ ........ (II) Write the expression of unit vector in y ′ axis. j ′ = i sin β + j cos β Substitute i sin β + j cos β for j ′ in Equation (II). H G = ( 1 3 m b 2 ) ( ω cos β ) ( i sin β + j cos β ) ......... (III) Write the expression of rate of change of angular momentum of the system. H ˙ G = ( H ˙ G ) G x y z + ( Ω × H G ) ........ (IV) Here, the angular acceleration is Ω . Write the expression of angular acceleration. Ω = ω = 0 Substitute 0 for Ω and ( 1 3 m b 2 ) ( ω cos β ) ( i sin β + j cos β ) for H G in Equation (IV). H ˙ G = ( H ˙ G ) G x y z + ( ( 0 ) ( ( 1 3 m b 2 ) ( ω cos β ) ( i sin β + j cos β ) ) ) = ( H ˙ G ) G x y z + 0 = ( H ˙ G ) G x y z To determine (b) The dynamic reactions at C . The dynamic reactions at D .

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 18.71P

To determine

(a)

The angular acceleration of the assembly.

To determine

(b)

The dynamic reactions at C.

The dynamic reactions at D.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 18.2, Problem 18.70P

Chapter 18.2, Problem 18.72P

Students have asked these similar questions

-6- 8 من 8 Mechanical vibration HW-prob-1 lecture 8 By: Lecturer Mohammed O. attea The 8-lb body is released from rest a distance xo to the right of the equilibrium position. Determine the displacement x as a function of time t, where t = 0 is the time of release. c=2.5 lb-sec/ft wwwww k-3 lb/in. 8 lb Prob. -2 Find the value of (c) if the system is critically damping. Prob-3 Find Meq and Ceq at point B, Drive eq. of motion for the system below. Ш H -7~ + 目 T T & T тт +

Q For the following plan of building foundation, Determine immediate settlement at points (A) and (B) knowing that: E,-25MPa, u=0.3, Depth of foundation (D) =1m, Depth of layer below base level of foundation (H)=10m. 3m 2m 100kPa A 2m 150kPa 5m 200kPa B

W PE 2 43 R² 80 + 10 + kr³ Ø8=0 +0 R²+J+ kr200 R² + J-) + k r² = 0 kr20 kr20 8+ W₁ = = 0 R²+1) R²+J+) 4 lec 8.pdf Mechanical vibration lecture 6 By: Lecturer Mohammed C. Attea HW1 (Energy method) Find equation of motion and natural frequency for the system shown in fig. by energy method. m. Jo 000 HW2// For the system Fig below find 1-F.B.D 2Eq.of motion 8 wn 4-0 (1) -5- m

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 author explains the angular acceleration of the assembly.