(a) Explanation Given information: The weight ( W ) of the rod is 10 lb. The angular velocity ( ω x ) of the shaft is 12 rad/s . Calculation: Find the mass ( m ) of the rod using the equation: m = W g Here, g is the acceleration due to gravity. Substitute 10 lb for W and 32.2 ft/s 2 for g . m = 10 32.2 = 0.31056 lb ⋅ s 2 /ft Write the vector form of angular velocity ( ω ) : ω = ω x i + ω y j + ω z k Substitute 12 rad/s for ω x , 0 for ω y , and 0 for ω z . ω = ( 12 ) i + 0 + 0 = ( 12 rad/s ) i (1) Consider G is the mass center of the assembly. The shaft divided into 8 sections, each of length, a and mass m ′ . Sketch the system as shown in Figure (1). Refer Figure (1), Find the each length of section ( a ) in feet. a = ( 10 in . ) × ( 1 ft 12 in . ) = 0.8333 ft Find the mass of section ( m ′ ) m ′ = m 8 Substitute 0.31056 lb ⋅ s 2 /ft for m . m ′ = 0.31056 8 = 0.03882 lb ⋅ s 2 /ft Find the mass moment of inertia ( I ¯ x ) about x -axis using the equation: I ¯ x = ( 4 ) ( 1 3 m ′ a 2 ) + 2 ( m ′ a 2 ) = 10 3 m ′ a 2 Substitute 0.03882 lb ⋅ s 2 /ft for m ′ and 0.8333 ft for a . I ¯ x = 10 3 ( 0.03882 ) ( 0.8333 ) 2 = 0.0898 lb ⋅ s 2 ⋅ ft Find the mass moment of inertia ( I ¯ x y ) about xy -axis using the equation: I ¯ x y = 0 Find the mass moment of inertia ( I ¯ x z ) about xz -axis using the equation: I ¯ x z = ( 4 ) ( m ′ a a 2 ) = 2 m ′ a 2 Substitute 0.03882 lb ⋅ s 2 /ft for m ′ and 0.8333 ft for a . I ¯ x z = 2 ( 0.03882 ) ( 0.8333 ) 2 = 0.053912 lb ⋅ s 2 ⋅ ft Find the x -component of the angular momentum ( H G ) x of the assembly about its mass center G . ( H G ) x = I ¯ x ω Substitute 0 (b) To determine Find the angle formed by H G and AB .

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ISBN: 9781260663778

Author: BEER

Publisher: MCG

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Chapter 18.1, Problem 18.17P

(a)

To determine

The angular momentum HG of the shaft about its mass center G.

(b)

To determine

Find the angle formed by HG and AB.

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Chapter 18.1, Problem 18.16P

Chapter 18.1, Problem 18.18P

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The angular momentum H G of the shaft about its mass center G .

Solution Summary: The author calculates the angular momentum of the shaft about its mass center G using the equation: m=Wg.