Explanation Given information: The weight ( W ) of rod AB is 5 lb. The length ( L ) of rod AB is 30 inch. The angle ( β ) formed by rod AB with vertical is 30 ° . The velocity ( v 1 ) of the rod AB is 8 ft/s. Calculation: Find the mass ( m ) of the uniform slender rod AB : m = W g Here, g is the acceleration due to acceleration due to gravity. Substitute 5 lb for W and 32.2 ft / s 2 for g . m = 5 lb 32.2 ft / s 2 = 0.155279 lb ⋅ s 2 / ft Find the centroidal moment of inertia ( I ¯ ) of the uniform slender rod AB using the equation: I ¯ = 1 12 m L 2 Substitute 0.155279 lb ⋅ s 2 / ft for m and 30 in. for L . I ¯ = 1 12 ( 0.155279 ) ( 30 in . × 1 ft 12 in . ) 2 = 80.875 × 10 − 3 lb ⋅ s 2 ⋅ ft Sketch the free body diagram of the uniform slender rod AB after impact as shown in Figure (1). Find the equation of the velocity of the mass center G of the uniform slender rod AB . v G = L 2 ω Here, ω is the angular velocity of the uniform slender rod AB after impact Substitute 30 in. for L . v G = ( 30 in . × 1 ft 12 in . ) 2 ω = 1.25 ω Consider the principle of impulse and momentum. Syst Momenta 1 + Syst Ext Imp 1y2 = Syst Momenta 2 Sketch the impulse and momentum diagram of the rod AB as shown in Figure (2).

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Chapter 17.3, Problem 17.104P

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Find the angular velocity of the rod immediately after the impact.

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Chapter 17 Solutions

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Find the angular velocity of the rod immediately after the impact.

Solution Summary: The author calculates the angular velocity of the uniform slender rod AB using the equation: m=Wg.

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