(a) Explanation Given information: The length of slender rod is l . The distance of point C from mass center G is b . The mass of the rod is m . Calculation: Write the equation of mass moment of inertia of rod. I = 1 12 m l 2 Sketch the initial 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. The rod is in horizontal position. Therefore, the potential energy ( V 1 ) of the rod is zero. Sketch the final position of the system as shown in Figure (2). Refer Figure (2), Write the equation of velocity ( v ¯ 2 ) at final position of the rod. v ¯ 2 = b 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 b ω 2 for v ¯ 2 and 1 12 m l 2 for I . T 2 = 1 2 m ( b ω 2 ) 2 + 1 2 ( 1 12 m l 2 ) ω 2 2 = 1 2 m ( b 2 + 1 12 l 2 ) ω 2 2 The elevation change ( h ) from initial to final position is − b . Write the equation of potential energy ( V 2 ) of rod at final position. V 2 = m g h Substitute − b for h . V 2 = m g ( − b ) = − m g b Apply the Principle of conservation of energy. T 1 + V 1 = T 2 + V 2 Substitute 0 for T 1 , 0 for V 1 , 1 2 m ( b 2 + 1 12 l 2 ) ω 2 2 for T 2 , and − m g b for V 2 (b) To determine Find the corresponding values of its angular velocity and of the reaction at C .

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ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 17.1, Problem 17.17P

(a)

To determine

The distance b for which the angular velocity of the rod as it passes through a vertical position is maximum.

(b)

To determine

Find the corresponding values of its angular velocity and of the reaction at C.

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Chapter 17.1, Problem 17.16P

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