(a) Explanation Given information: The two identical rods are connected by a pin at B . Calculation: Assume the angular velocity as ω A B = ω B C = 0 . Calculate the mass moment of inertia ( I ¯ ) as shown below. I ¯ = 1 12 m L 2 Sketch the Free Body Diagram as shown in Figure 1. Refer to Figure 1. The accelerations ( a A ) x = ( a ¯ A B ) x = ( a B ) x = ( a ¯ B C ) x = a C . Calculate the acceleration of BC ( a ¯ B C ) y as shown below. ( a ¯ B C ) y = L 2 α B C Calculate the acceleration at B ( a ¯ B ) y as shown below. ( a ¯ B ) y = L α B C (1) Calculate the acceleration of AB ( a ¯ A B ) y as shown below. ( a ¯ A B ) y = ( a ¯ B ) y + L 2 α A B Substitute L α B C for ( a ¯ B ) y . ( a ¯ A B ) y = L α B C + L 2 α A B Calculate the acceleration at A ( a ¯ A ) y as shown below. ( a ¯ A ) y = ( a ¯ B ) y + L α A B Substitute L α B C for ( a ¯ B ) y . ( a ¯ A ) y = L α B C + L α A B (2) Sketch the kinetic Free Body Diagram of the entire system as shown in Figure 2. Refer to Figure 2. Apply the Equilibrium of forces along x direction as shown below. ∑ F x = m a x 0 = m ( a ¯ A B ) x + m ( a ¯ B C ) x 0 = 2 m a ¯ C a ¯ C = 0 Hence, the accelerations as ( a A ) x = ( a ¯ A B ) x = ( a B ) x = ( a ¯ B C ) x = 0 . Sketch the Free Body Diagram of the rod AB as shown in Figure 3. Refer to Figure 3. Apply the Equilibrium of moment about B as shown below. ∑ M B = I G α + m a d 1 2 m g L = I ¯ α A B + m ( a ¯ A B ) y × L 2 Substitute 1 12 m L 2 for I ¯ and L α B C + L 2 α A B for ( a ¯ A B ) y . 1 2 m g L = 1 12 m L 2 α A B + m × ( L α B C + L 2 α A B ) × L 2 1 2 g = 1 12 L α A B + L 2 α B C + L 4 α A B g = 2 L α A B × ( 1 + 3 12 ) + L α B C 2 3 L α A B + L α B C = g (3) Apply the Equilibrium of forces along y direction as shown below. ∑ F y = m a y B − m g = − m ( a ¯ A B ) Substitute 1 12 m L 2 for I ¯ and L α B C + L 2 α A B for ( a ¯ A B ) (b) To determine Find the acceleration of point B .

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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

Publisher: McGraw-Hill Education

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Chapter 16.2, Problem 16.150P

(a)

To determine

Find the acceleration of point A.

(b)

To determine

Find the acceleration of point B.

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Chapter 16.2, Problem 16.149P

Chapter 16.2, Problem 16.151P

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Vector Mechanics for Engineers: Statics and Dynamics

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Find the acceleration of point A .

Solution Summary: The author calculates the mass moment of inertia of the two identical rods connected by a pin at B.