Explanation Given information: The figure shown below shows the free body diagram of the system Figure-(1) Write the expression for the rate change of momentum. H ˙ G = H G x y z + Ω × H G .........(I) Here, the rate of change of angular momentum is H ˙ G , angular momentum with respect to the frame of reference and angular velocity of the xyz frame is Ω . Write the expression for the angular momentum about the centre of mass. H G = I x ω i + I x y ω j + I x z ω k ……. (II) Here, momentum of inertia about x direction is I x , momentum of inertia about x y plane is I x y , momentum of inertia about x z plane is I x z and the angular velocity is x z . Substitute I x ω i + I x y ω j + I x z ω k for H G , ω i for Ω and 0 for H G x y z in Equation (I). H ˙ G = 0 + ω i × ( I x ω i + I x y ω j + I x z ω k ) = I x z ω j + I x y ω k ……. (III) The shaft lies between x z plane hence the value of I x y is 0 . Substitute 0 for I x y in Equation (III). H ˙ G = I x z ω 2 j + ( 0 ) ω 2 k = I x z ω 2 j .........(IV) The magnitude of A and B is Equal and opposite in direction because the center of mass lies on the line A B as it is symmetrical A and B forms a couple. A = − ( B ) .........(V) Write the expression for the force at B . F B = 4 a i × ( B y j + B z k ) = 4 a B y k − 4 a B z j .........(VI) The magnitude of B in the y direction is 0 . Substitute 0 for B y in Equation (VI). F B = 0 − 4 a B z j = − 4 a B z j .........(VII) Here, the magnitude of couple at B is F B the distance between a A to B is 4 a .the magnitude of B in z direction is B z

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,

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Chapter 18.2, Problem 18.68P

To determine

The dynamic reaction at A.

The dynamic reaction at point B.

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Chapter 18.2, Problem 18.67P

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