(a) Explanation Given information: The length of slender rod is l . The weight of the rod is W . The mass of the rod is m . Calculation: Write the general equation of mass ( m ) of the rod. m = W g Here, g is the acceleration due to gravity. Write the equation of mass moment of inertia of rod. I = 1 12 m l 2 Sketch the initial and final position of the system as shown in Figure (1). Refer Figure (1), At initial position, the system is at rest. Therefore, the velocity ( v ¯ 1 ) , angular velocity ( ω 1 ) , and kinetic energy ( T 1 ) of the rod are zero. Write the equation of velocity ( v ¯ 2 ) at final position of the rod. v ¯ 2 = l 2 ω 2 Here, ω 2 is the angular velocity of rod at final position. Write the equation of kinetic energy ( T 2 ) of rod at final position. T 2 = 1 2 m v ¯ 2 2 + 1 2 I ω 2 2 Substitute l 2 ω 2 for v ¯ 2 and 1 12 m l 2 for I . T 2 = 1 2 m ( l 2 ω 2 ) 2 + 1 2 ( 1 12 m l 2 ) ω 2 2 = 1 8 m l 2 ω 2 2 + 1 24 m l 2 ω 2 2 = 1 6 m l 2 ω 2 2 Write the equation of work done ( U 1 → 2 ) of the system. U 1 → 2 = m g l 2 Apply the Principle of work and energy. T 1 + U 1 → 2 = T 2 Substitute 0 for T 1 , m g l 2 for U 1 → 2 , and 1 6 m l 2 ω 2 2 for T 2 (b) To determine The angular velocity and corresponding reaction at the pivot of the rod as it passes through a vertical position if W = 1.8 lb and l = 3 ft .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

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

Publisher: McGraw-Hill Education

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Chapter 17.1, Problem 17.16P

(a)

To determine

Find the angular velocity of the rod as it passes through a vertical position.

Find the corresponding reaction at the pivot.

(b)

To determine

The angular velocity and corresponding reaction at the pivot of the rod as it passes through a vertical position if W=1.8 lb and l=3 ft.

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Chapter 17.1, Problem 17.15P

Chapter 17.1, Problem 17.17P

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Find the angular velocity of the rod as it passes through a vertical position. Find the corresponding reaction at the pivot.