Explanation Given: Mass of the rod is m and length of the rod is L . Concept used: Expression for change of angular momentum is given as follows: H G = H x i + H y j + H z k ........ (1) Here, change in momentum is H G . Expression for rate of change of angular momentum is given as follows: H ˙ G = ( H ˙ G ) G x y z + ( Ω × H G ) ........ (2) Here, rate of change in momentum is H ˙ G . Calculation: Moment of inertia is calculated as follows: I x = I z = 1 12 m L 2 and I y = 0 Component of H G along x direction is calculated as follows: H x = I x ω 1 cos θ × sin θ H x = − 1 12 m L 2 ω 1 cos θ × sin θ Component of H G along y direction is calculated as follows: H y = I y ω y H y = 0 Component of H G along z direction is calculated as follows: H z = I z ω 2 H z = 1 12 m L 2 ω 2 Substitute − 1 12 m L 2 ω 1 cos θ × sin θ for H x , 0 for H y and 1 12 m L 2 ω 2 for H z in equation (1). H G = − 1 12 m L 2 ω 1 cos θ × sin θ i + 0 j + ( 1 12 m L 2 ω 2 ) k H G = − 1 24 m L 2 ω 1 sin 2 θ i + ( 1 12 m L 2 ω 2 ) k Angular velocity of the reference frame can be calculated as follows: Ω = ω x i + ω y j Ω = 0 i + ω 1 j Substitute − 1 24 m L 2 ω 1 ( 2 cos 2 θ ) i + ( 1 12 m L 2 ω 1 ) ( − 2 ω 2 cos θ sin θ ) j for ( H ˙ G ) G x y z and − 1 24 m L 2 ω 1 sin 2 θ i + ( 1 12 m L 2 ω 2 ) k for H G in equation (2) To determine (b) The couple M 2 . To determine (c) Dynamic reactions at C and 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,

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Chapter 18.2, Problem 18.106P

To determine

(a)

The couple M1.

To determine

(b)

The couple M2.

To determine

(c)

Dynamic reactions at C and D.

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Chapter 18.2, Problem 18.105P

Chapter 18.3, Problem 18.107P

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