Explanation Given information: The length of the homogeneous cylinder ( L ) is 30 m. The radius of the homogeneous cylinder ( a ) is 3 m. The precession rate of the station about the fixed direction GD is 2 rev/h . Calculation: Determine the ratio of ( I I ′ ) . Here, I is the moment of inertia of the cylinder about its spin axis and I ′ is the moment of inertia of the cylinder about its transverse axis. Substitute 1 2 m a 2 for I and 1 12 m ( 3 a 2 + L 2 ) for I ′ . ( I I ′ ) = 1 2 m a 2 1 12 m ( 3 a 2 + L 2 ) = 6 a 2 ( 3 a 2 + L 2 ) (1) Substitute 30 m for L and 3 m for a in Equation (1). ( I I ′ ) = 6 ( 3 ) 2 ( 3 ( 3 ) 2 + ( 30 ) 2 ) = 0.05825 Determine the angle γ using steady precession with no force. tan γ = I I ′ tan θ Here, θ is the angle of axis. Substitute 0.05825 for I I ′ and 40 ° for θ . tan γ = 0.05825 tan 40 ° γ = tan − 1 ( 0.05825 tan 40 ° ) γ = 2

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ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 18.3, Problem 18.126P

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The rate of spin of the station about its axis of symmetry CC′.

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Chapter 18.3, Problem 18.125P

Chapter 18.3, Problem 18.127P

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The rate of spin of the station about its axis of symmetry C C ′ .

Solution Summary: The author calculates the rate of spin of the station about its axis of symmetry CCprime .

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The rate of spin of the station about its axis of symmetry CC′.

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