(a) Explanation Given information: The mass of each disk ( m ) is 5 kg. The radius ( r ) of each disk is 300 mm. The angular velocity ( ω 1 ) of the disk is 1,200 rpm. The angular velocity ( ω 2 ) of the rod AB is 60 rpm. The length ( c ) between the shafts C and D is 0.6 m. Calculation: Find angular velocity ( ω 1 ) of the disk in rad/s. ω 1 = 1 , 200 rev min × 2 π rad 1 rev × 1 min 60 s = 125.6637 rad/s Find angular velocity ( ω 2 ) of the rod AB in rad/s. ω 2 = 60 rev min × 2 π rad 1 rev × 1 min 60 s = 6.2832 rad/s Consider anticlockwise rotation is positive. The angular velocity ( ω x ) of the system along x -axis is zero. Write the equation of angular velocity ( ω y ) of the system along y -axis. ω y = ω 1 Write the equation of angular velocity ( ω z ) of the system along z -axis. ω z = − ω 2 Find the vector form of angular velocity ( ω A ) of the system about disk A ω A = ω x i + ω y j + ω z k Substitute 0 for ω x , ω 1 for ω y , and − ω 2 for ω z . ω A = ( 0 ) i + ( ω 1 ) j + ( − ω 2 ) k = ω 1 j − ω 2 k (1) Write the equation of angular momentum of system about A ( H A ) . H A = I ¯ x ω x i + I ¯ y ω y j + I ¯ z ω z k Substitute 0 for ω x , ω 1 for ω y , and − ω 2 for ω z . H A = I ¯ x ( 0 ) i + I ¯ y ( ω 1 ) j + I ¯ z ( − ω 2 ) k = I ¯ y ω 1 j − I ¯ z ω 2 k Write the angular velocity of reference frame Oxyz about z -axis ( Ω ) . Ω = − ω 2 k The rate of change of angular momentum ( H ˙ A ) O x y z about the reference frame is 0. Write the equation of rate of change of angular momentum ( H ˙ A ) of the system about A . H ˙ A = ( H ˙ A ) O x y z + Ω × H A Substitute 0 for ( H ˙ A ) O x y z , − ω 2 k for Ω , and I ¯ y ω 1 j − I ¯ z ω 2 k for H A . H ˙ A = 0 + ( − ω 2 k ) × ( I ¯ y ω 1 j − I ¯ z ω 2 k ) = I ¯ y ω 2 ω 1 i + 0 = I ¯ y ω 2 ω 1 i (2) Find the mass moment of inertia ( I ¯ y ) of the disk about y -axis using the equation: I ¯ y = 1 2 m r 2 The angular velocity of disk A and B is same (b) To determine The dynamic reactions at points C and D if the direction of spin of disk A is reversed.

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 18.2, Problem 18.95P

(a)

To determine

The dynamic reactions at points C and D.

(b)

To determine

The dynamic reactions at points C and D if the direction of spin of disk A is reversed.

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Chapter 18.2, Problem 18.94P

Chapter 18.2, Problem 18.96P

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Chapter 18 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 18.1 - A thin, homogeneous disk of mass m and radius r...Ch. 18.1 - Prob. 18.2P Ch. 18.1 - 18.3 Two uniform rods AB and CE, each of weight 3...Ch. 18.1 - A homogeneous disk of weight W = 6 lb rotates at...Ch. 18.1 - Prob. 18.5P Ch. 18.1 - A solid rectangular parallelepiped of mass m has a...Ch. 18.1 - Prob. 18.8P Ch. 18.1 - Determine the angular momentum HD of the disk of...Ch. 18.1 - Prob. 18.10P Ch. 18.1 - Prob. 18.11P

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The dynamic reactions at points C and D .

Solution Summary: The author analyzes the dynamic reactions at points C and D.