Explanation Given information: The mass ( m ) of the rod is 3 kg. The length ( L ) of the rod is 800 mm. The height ( h ) of cylinder DE is 240 mm. The angular velocity ( ω ) of the assembly is 40 rad/s. The velocity ( v B ) of rod at end B is 75 mm/s. The centroidal mass moment of inertia ( I ¯ D E ) of the cylinder about a vertical axis is 0.025 kg ⋅ m 2 . Calculation: Draw the geometry of the initial and final position of the rod with components of velocity as shown in Figure 1. Find the initial velocity ( v ¯ 1 ) of the assembly using kinematics. v ¯ 1 = ( 400 mm × 1 m 1 , 000 mm ) ω 1 Substitute 40 rad/s for ω 1 . v ¯ 1 = ( 400 mm × 1 m 1 , 000 mm ) ( 40 ) = 1.6 m/s Find the final velocity ( v ¯ 2 ) of the assembly using kinematics. v ¯ 2 = ( 280 mm × 1 m 1 , 000 mm ) ω 2 = 0.28 ω 2 Find the centroidal mass moment of inertia ( I ¯ A B ) of the rod AB using the equation: I ¯ A B = 1 12 m L 2 Substitute 3 kg for m and 800 mm for L . I ¯ A B = 1 12 ( 3 ) ( 800 mm × 1 m 1 , 000 mm ) 2 = 0.16 kg ⋅ m 2 Consider the conservation of angular momentum about C . Sketch the momentum diagram of the assembly as shown in Figure (2)

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ISBN: 9781260804638

Author: BEER

Publisher: MCG

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Chapter 17.2, Problem 17.82P

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Find the angular velocity of the assembly as end B of the rod strikes end E of the cylinder.

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Chapter 17.2, Problem 17.81P

Chapter 17.2, Problem 17.83P

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Find the angular velocity of the assembly as end B of the rod strikes end E of the cylinder.

Solution Summary: The author calculates the angular velocity of the assembly as end B strikes end E of a cylinder using kinematics.

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Find the angular velocity of the assembly as end B of the rod strikes end E of the cylinder.

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